# How do you integrate [(x^2)(cos(2(x^3)))]?

5,216 results

### Mathematics-Integration

Question: Prove that [integrate {x*sin2x*sin[π/2*cos x]} dx] /(2x-π) } from (0-π) = [ integrate {sin x*cos x*sin[π/2*cos x} dx ] from (0-π). My thoughts on the question: We know that integrate f(x) dx from (0-a) = integrate f(a-x) dx from (0-a) From that and by sin(2x)=...

### Integral calculus

Please can anyone help with the following problems - thanks. 1) Integrate X^4 e^x dx 2) Integrate Cos^5(x) dx 3) Integrate Cos^n(x) dx 4) Integrate e^(ax)Sinbx dx 5) Integrate 5xCos3x dx The standard way to solve most of these integrals is using partial integration. So, look ...

### Calc 1

integrate from 0 to pi/4 (sec^2x)/((1+7tanx)^2)^1/3 integrate form pi^2/36 to pi^2/4 (cos(x^1/2))/(xsin(x^1/2))^1/2 integrate from 0 to pi/3 (tanx)/(2secx)^1/2

### calculus

1) Integrate Cos^n(x) dx 2) Integrate e^(ax)Sinbx dx 3) Integrate (5xCos3x) dx I Will be happy to critique your thinking on these. 1) Derive a recursive relation. 2) Simplest by replacing sin(bx) by Exp[i b x] and taking imaginary part at the end. 3) First integrate sin(yx) ...

### Calculus

How do you integrate [(x^2)(cos(2(x^3)))]? I tried to integrate by parts but I'm going in circles yet again...

### PLZ integrate

integrate cos^3x dx tnk U

### Integral calculus

Please do help solve the followings 1) Integrate e^4 dx 2) Integrate dx/sqrt(90^2-4x^2) 3) Integrate (e^x+x)^2(e^x+1) dx 4) Integrate xe^x2 dx e^4 is a constant. 3) let u= e^x + x du= (e^x + 1)dx 4) let u= x du=dx v= e^x dv= e^x dx

### math

integrate sqrt(2((sin(x))^2 + 50((cos(x))^2 - 10sin(x)cos(x))

### Math

integrate (sin^8 x - cos^8 x)/(1 - 2sin^2 x * cos^2 x) w.r.t. x

### Trig Identities

Why does cos^2(x)= 1/2cos(2x)+1/2? I am trying to integrate, but the answer key says to first rewrite the expression like the above. I don't get how to change cos^2(x) into that. Explain?

### Maths

keep getting stuck for integrate e^(bx) cos x i get = cos x e^bx/b - int -sin x e^bx/b = cos x e^bx/b - -sin x e^bx/b^2 - int - cos x e^bx/b^2 this is where i get stuck please help

### math

the question asks to integrate cos(t)/ (5sin(t)+8)^2 the answer i got was xcos(t)/(5sin(t)+8)^2 this is not right i believe there is something wrong with the x in front of the cos.... please heplp

### integrate

integrate du/3u and integrate x/x^2 dx it might be simple...i just need a head start...tnx

### Mathematics -Integration : to Steve

But how do we integrate ln|1+tanx| da X=theta =int.[ln|cos x|dx] +int.[sin x| dx ] - int.[ln|cos x| dx] ?

### math

integrate Cos^7(2x)

### Calculus

Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help.

### college math

how do you integrate (cos^2 x)^4

### Math

Integrate (sin^2(t)+1)/(cos^4(t))dt

### Calculus

Integrate [sinx/(1+cos^2(x))] from pi/2 to pi.

### maths

integrate -sinx/ã4+cos^2x dx

### Integration need help

Integrate (6x^2-cos(2x))dx??

### Calculus

Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help. Calculus - Steve, Tuesday, January 12, 2016 at 12:45am 1/2 ∫ 1/(sin(x/2)cos(x/2))dx let u...

### Calculus

6.] Replace the integral in exercise 5 (int. (1/ 1 – t) dt a = 0, b = 1/2with ?1/(1+t) dt with a = 0, b = 1, and repeat the four steps. a. integrate using a graphing utility b. integrate exactly c. integrate by replacing the integrand with a Taylor series and integrate term ...

### Math

Find the greatest value of a,so that integrate [x*root{(a^2-x^2)/(a^2+x^2)} ] from 0-a<=(π-2) Let I =integrate{ [x*root{(a^2 - x^2)/(a^2+x^2)}]dx } from 0-a I used the substitution u=root[x^2+a^] to simplify the further. After substituting and changing limits I got, I=...

### Math

Integrate: ∫(cos^3 x)^2 dx

### Calculus

How do we integrate [(cosx)^2(nx)(sin(nx))]/[a-(cos(nx))] dx?

### calculus 2

Justify, with a written explanation or a mathematical reasoning and with a sketch of at least two different cases, the following properties of integrals: a) If f(x) is less than or equal to g(x) for a<=x<=b then integrate from a to b of f(x)dx is less than or equal to ...

### Mathematics-Integration

Question: For any positive integer n,show that integrate.[(sin x)^2n dx ] from o - π/2 = [(2n)!*π]/[(2)^(2n+1)*(n!)^2 ] What I thought: Let I =int.[(sinx)^2n dx] And again I= int.[ (sin(π/2-x))^2n dx] = int.[ (cos)^2n dx] 2I= int.[(sin x)^2n + (cos x)^2n dx] 2I= int.[ (sin ...

### Calculas

Integrate: Cos^7(2x) Explanation would be helpful

### Calculus

Integrate Cos^7(2x) Explanation would be helpful

### Calculus - MathMate Please help

ok, i tried to do what you told me but i cant solve it for c because they cancel each others out! the integral for the first one i got is [sin(c)cos(x)-cos(c)sin(x)+sin(x)+c] and the integral for the 2nd one i got is [-sin(c)cos(x)+cos(c)sin(x)-sin(x)+c] I don't know what to ...

### calculus

integrate it by integrating factor (cos^3x)dy/dx +ycosx=sinx

### Calc.

Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= [(cos^x(x))(ln(cos(x)))-(x sin(x)cos^(x-1...

### calculus

Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= [(cos^x(x))(ln(cos(x)))-(x sin(x)cos^(x-1...

### math

Determine exact value of cos(cos^-1(19 pi)). is this the cos (a+b)= cos a cos b- sina sin b? or is it something different. When plugging it in the calculator, do we enter it with cos and then the (cos^-1(19 pi)).

### Calculus

Can someone help me to integrate by substitution the indefinite integral: (sinx)/ (1+cos(^2)x)?

### calculus

We are not going to do that work for you, but will be glad to help you. The unit sphere is the sphere with radius 1 centered in the origin. They give you the coordinates of a vector. Compute the dot product of the vector and the local surface area normal and integrate it over ...

### Math

integrate dy/dx=x(y^(1/2))(cos^2(y^(1/2))^2) I know I need to separate, and Iv'e moved dx to the right side with dy on the left. Don't know how to go on.

### pre-cal

Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x -48 cos^4 x + 18 cos^2 x - 1 I assume you are ...

### Math

Solve it showing detail steps..please. Integrate : ∫(cos^3 x)^2 dx

### Math Integration

i keep getting stuck and i think im missing something integrate by parts e^(bx) cos x dx thanks

### Adv Calculus

Integrate the following indefinite integral: (sin7x)^12 * (cos7x)^3 Hint: sin^2 + cos^2 = 1

### Math

Please help me the way through this sum Integrate Cos squared(3x) btwn x=pie/2 andx=0

### calculus help

integrate cos^10xdx.. .plz show working i really wanna learn these thanks anyway

### maths

Find the roots of z^6 + 1 and hence resolve z^6 + 1into read quadratic factors; deduce that cos3x = 4[cos(x) -cos(pi/6)][(cos(x) -cos(pi/2)][(cos(x) -cos(5pi/6)]

### maths

Find the roots of z^6 + 1 and hence resolve z^6 + 1into read quadratic factors; deduce that cos3x = 4[cos(x) -cos(pi/6)][(cos(x) -cos(pi/2)][(cos(x) -cos(5pi/6)]

### Calc

How do you solve ∫sin(3x+4)dx? I got the -cos(3x+4) part, but do you have to integrate the 3x+4 too? Does chain rule apply?

### Calculus

Use the trapezoidal rule with n = 5 to approximate. Keep at least 2 decimal places accuracy. Integrate: (cos(x))/(x) from x=1 to 5

### Calculus

Use Simpson's rule with n = 4 to approximate. Keep at least 2 decimal places accuracy. Integrate: (cos(x))/(x) x=1 to 5

### Math - Solving Trig Equations

What am I doing wrong? Equation: sin2x = 2cos2x Answers: 90 and 270 .... My Work: 2sin(x)cos(x) = 2cos(2x) sin(x) cos(x) = cos(2x) sin(x) cos(x) = 2cos^2(x) - 1 cos(x) (+/-)\sqrt{1 - cos^2(x)} = 2cos^2(x) - 1 cos^2(x)(1 - cos^2(x)) = 4cos^4(x) - 4cos^2(x) + 1 5cos^4(x) - 5cos^...

### calculus very hard help

integrate:cos^10xdx even with the previous hint a tutor here gave me i still don,t know it

### TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 x = (sin^2x)^3 + (cos^2x)^3 = (sin^2x+cos...

### Fourier Sine Series Q

I have the function f(x) = cos(x) on the interval from 0 to pi and I need to comput the Fourier sine series. I have the integral of cos(x) multiplied by sin(nx), I can't figure out a way to integrate them! The "n" gets in the way, what do I do?

### calc

find the area between the x-axis and the graph of the given function over the given interval: y = sqrt(9-x^2) over [-3,3] you need to do integration from -3 to 3. First you find the anti-derivative when you find the anti-derivative you plug in -3 to the anti-derivative and ...

### Mathematics - Trigonometric Identities

Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y)(sin^2y) / (sin^...

### calculus help please

dy/dx = 2y^2 Integrating...y=2/3 y^3 + C put 1,-1 into the equation, and solve for C. Then find the y for x=2 if y= a^uhttp://math2.org/math/integrals/tableof.htm see exponential functions. dy/dx=2y^2 and if y=-1 when x=1, then when x=2, y=? how do i get x in the equation. do ...

### trig

Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity = sin(145-75) = sin 70 = cos 20 note that...

### Precalculus

Solve Cos^2(x)+cos(x)=cos(2x). Give exact answers within the interval [0,2π) Ive got the equation down to -cos^2(x)+cos(x)+1=0 or and it can be simplified too sin^2(x)+cos(x)=0 If you could tell me where to go from either of these two, it would be great help.. Thankyou ...

### math

Find the exact value of cos 300 degrees. thanks guys cos 300 = 1/2 = 0.500 how do you know? I am supposed to show my work. You ought to know the rule on 30-60-90 triangles. If the hyp is 2, the shorter side is 1, and the longer side is sqrt3. what does that have to do with ...

### Trigonometry

Write equivalent equations in the form of inverse functions for a.)x=y+cos è b.)cosy=x^2 (can you show how you would solve) a.) x= y+ cos è cos è = x-y theta = cos^-1(x-y) b.) cosy=x^2 cos(y) = x^2 y = Cos^-1(x^2)

### tigonometry

expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) Add the two equations: sin(a+b) + sin(a-b) = ...

### Math Integration

Integrate: f (x)/(2x + 1) dx let f represent integrate sign let u = x, du = dx => dx = du = f (u)/(2u + 1) du = f u (2u + 1)^(-1) du = (1/2)u^2 (ln|2u + 1|) + c = (1/2)x^2 (ln|2x + 1|) + c ...what did I do wrong? The correct answer is (1/2)x - (1/4)ln|2x + 1| + c

### Calculus AB

Please help me integrate this equation using partial fractions: Integrate [(x^2+5)/(x^3-x^2+x+3)]dx. Thank you very much.

### trig

Show that 1-cos2A/Cos^2*A = tan^2*A 1-cos2A/Cos^2*A = [Cos^2(A) - Cos(2A)]/Cos^2(A). Substitute: Cos(2A) = 2Cos^2(A) - 1: [1 - Cos^2(A)]/Cos^2(A)= Sin^2(A)/Cos^2(A) = tan^2(A)

### calc

integrate (3+x)x^(1/2)dx=? please help I have no idea how to integrate this problem

### Algebra

Write an equation for the translation of the function. y = cos x; translated 6 units up A. y = cos x- 6 B. y = cos(x + 6) C. y = cos x + 6 D. y = cos(x 6) I think its B or c..

### math

if cos(B-C)+cos(C-A)+cos(A-B)=-3/2 then prove that cosA+cosB+cosC=O and sinA+sinB+sinC=O after that prove that cos(B-C)=cos(C-A)=cos(A-B)=-1/2

### plz integrate

how do u integrate 1+u/3u+2u^2 please help me get started ...tnk u

### MATHS...PLEASE HELP

what do you get when you: integrate 10sin^4xcosx dx when you integrate 9x^2e^6x^3 dx

### algebra

Can someone please help me do this problem? That would be great! Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2 sin A I hope this will help. in my algebra ...

### Calculus

Integrate (1/2)sin(x^(1/2))dx. I've tried using u-substitution, with u=sin(x^(1/2)). du would then = ((1/2)x^(-1/2))(cos(x^(1/2))). As you can see, this only make the problem more complicated. I don't get what to do. Thank you in advance!

### Trigonometry

There is an arbitrary triangle with angles A, B, and C and sides of lengths a, b, and c. Angle A is opposite side a. How do I get the formulas: b * cos C + c * cos B = a c * cos A + a * cos C = b a * cos B + b * cos A = c Are these standard trig formulas? What are they called...

### Precal

I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A + cos A) ) = 1 - sin A cos A note that all the trig terms are closed right after there A's example sin A cos A = sin (A) cos (A) I wrote it out like this 0 = - sin^6 A - cos^6 A + 2sin^3 A cos^3 A - 2sin^3 ...

### Calc

Find the exact total of the areas bounded by the following functions: f(x) = sinx g(x) = cosx x = 0 x = 2pi I set my calculator to graph on the x-axis as a 2pi scale. The two functions appear to cross three times between x = 0 and 2pi. (including 2pi) Now, from top to bottom, ...

### Math

Explain how to do this with steps please. 1. Simplify cos(x-y)+cos(x+y)/cosx I did some of these so far, don't know if it is correct. Formula: cosxcosy= cos(x+y)+cos(x-y)/2 cos(x-y)+cos(x+y)/cosx =cosxcosy/2cosx

### Cos-Derivative

y= (cos^3 x) (cos 3x) I got -3 sin(3x) cos^3x - 3 sin(x) cos (3x) cos^2 (x) using the product rule Is this right? Thanks.

### Trig

Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos v + cos v sin u. cos (v - u) = cos u cos v + ...

### Calc II

For the following question, we need to find the length of the polar curve: r= 2/(1-cosx) from pi/2 </= x </= pi dr/dx= -2sinx/(1-cosx)^2 therefore the length would be expressed as follows: the integral from pi/2 to pi of (sqrt)[(2/(1-cos))^2 + (-2sinx/((1-cosx)^2))^2 ...

### Math

Prove each identity: a) 1-cos^2x=tan^2xcos^2x b) cos^2x + 2sin^2x-1 = sin^2x I also tried a question on my own: tan^2x = (1 – cos^2x)/cos^2x R.S.= sin^2x/cos^2x I know that the Pythagorean for that is sin^2x + cos^2x That's all I could do.

### math

the question asks to integrate cos(t)/(5sin(t)+8)^2 the answer i got was xcos(t)/(5sin(t)+8)^2 i think the x is wrong but i am not sure what i am doing wrong...help please.

### Math

Explain how to do this with steps please. 1. Simplify cos(x-y)+cos(x+y)/cosx Formula: cosxcosy= cos(x+y)+cos(x-y)/2 cos(x-y)+cos(x+y)/cosx =cosxcosy/2cosx

### Math

Find the exact value of cos 1 degree + cos 2 degrees + cos 3 degrees + ... + cos 357 + cos 358 degrees + cos 359 degrees.

### Trig

Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) =Sin-3/5 cos-3/5 = -0.46602 HELP ...

### maths

integrate by parts integrate (4+x^2)^1/2

### maths

integrate by parts integrate (4+x^2)^1/2

### Math - Solving for Trig Equations

Solve the following equation for 0 less than and/or equal to "x" less than and/or equal to 360 -- cos^2x - 1 = sin^2x -- Attempt: cos^2x - 1 - sin^2x = 0 cos^2x - 1 - (1 - cos^2x) = 0 cos^2x - 1 - 1 + cos^2x = 0 2cos^2x - 2 = 0 (2cos^2x/2)= (-2/2) cos^2x = -1 cosx = square ...

### Trig Help!

Question: Trying to find cos π/12, if cos π/6 = square root 3 over 2, how to find cos π/12 using DOUBLE angle formula? This is what I got so far.. cos 2(π/6) = cos (π/6 + π/6) = (cos π/6)(cos π/6) - (sin π/6)(sin π/6) = cos^2...

### Math (Integrals) (Volume of Revolution Setup)

I am supposed to find the area of the region given two boundaries and two functions revolving about the x axis. x = 0 x = pi/2 y = cos(x/2) y = sin(x/2) Graphing those two functions made me select to use the washer method. Therefore, I set my definite integral to this: pi∫[0...

### Math(Please check)

Use the fundamental identities to simplify the expression. tan^2 Q / sec^2 Q sin^2/cos^2 / 1/cos^2 = sin^2 / cos^2 times cos^2 / 1 = The cos^2 cancels out so sin^2 is left. Is this correct?

### Pre-Cal (Trig) Help?

The following relationship is known to be true for two angles A and B: cos(A)cos(B)-sin(A)sin(B)=0.957269 Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places. So I'm pretty lost on how to even begin this problem. I do know ...

### AP Calc B/C

Find the arc length of one arch of the sine curve. I started it by doing y=sinx, y'=cosx arc length= integral of sqrt(1+cos^2x)dx from pi/2 to 3pi/2 but I don't know how to integrate that! Thank you!

### Trig. Law of Cosines

Show that any triangle with standard labeling... a^2+b^2+c^2/2abc = cos(alpha)/a + cos(beta)/b + cos(gamma)/c I don't get it. Can someone please help me. Start here with the law of cosines: a^2 = b^2 + c^2 -2bc Cos A b^2 = a^2 + c^2 -2ac Cos B c^2 = a^2 + b^2 - 2ab Cos C Add ...

### Math

Solve this equation algebraically: (1-sin x)/cos x = cos x/(1+sin x) --- I know the answer is an identity, and when graphed, it looks like cot x. I just don't know how to get there. I tried multiplying each side by its conjugate, but I still feel stuck. This is what I have so ...

### Calculus Indefinite Intergral

I need help with integrating these two problems. Im stuck. 1. integrate (sin^-1)dx/((1-x^2)^3/2) sin^-1 aka arcsin 2. integrate dx/((1-x^2)^3/2) by using 1/z Any and all help will be appreciated!

### integral calculus

Integrate (((cos^2(x)*sin(x)/(1-sin(x)))-sin(x))dx thanks

### integral calculus

integrate: [ cos ^ 2 (x) * sin (x) / ( 1 - sin(x) )] - sin (x)

### math

Can you please check my work. A particle is moving with the given data. Find the position of the particle. a(t) = cos(t) + sin(t) s(0) = 2 v(0) = 6 a(t) = cos(t) + sin(t) v(t) = sin(t) - cos(t) + C s(t) = -cos(t) - sin(t) + Cx + D 6 = v(0) = sin(0) -cos(0) + C C=7 2= s(0) = -...

### Math

Show that for real x that {[cos x + 2 sin x + 1]/[cos x + sin x] } cannot have a value between 1 and 2. Let y = [(cos x+2 sin x + 1)/(cos x + sin x) ] y(cos x + sin x) = (cos x + 2 sin x + 1) sin x(y-2) + cos x(y-1)=1 , I just feel that this isn't the way to do this.. Any ...

### Calculus

which of the following integrals results from making the substitution u=x^3 in orer to find (squiggly vertical line)x^2cos(x^3)dx ~cos u du ~u^2 cos u du ~u^(2/3) cos u du1/3 os u du ~3 cos u du