Calculus
posted by Maria
Hello,
I'm having trouble with this exercise. Can you help me?
Integral of (x* (csc x)^2)dx
I'm using the uv  integral v du formula. I tried with u= (csc x)^2 and used some trigonometric formulas, but the expression became too complicated, I couldn't continue working. Then I tried with u=x, but the same happened.
Thank you in advance.
You are on the right track using integration by parts. Let u = x and let dv = csc^2 x dx = (1/sin^2 x) dx
du = x
v = cot x (You will have to prove that to yourself)
Integral u dv = uv  Integal v du
=  cot x  Integral (cot x dx)
=  cot x + log sin x
You will have to prove that Integral of cot x dx yourself also.
I have verified the steps and final answer with a table of integrals
Respond to this Question
Similar Questions

Trigonometry
Hello all, In our math class, we are practicing the trigonometric identities (i.e., sin^2(x)+cos^2(x)=1 or cot(x)=cos(x)/sin(x). Now, we are working on proofs that two sides of an equation are equal (for example, sin(x)*csc(x)=1; sin(x)csc(x)=sin(x)/sin(x)=1; … 
calculus
We're doing indefinite integrals using the substitution rule right now in class. The problem: (integral of) (e^6x)csc(e^6x)cot(e^6x)dx I am calling 'u' my substitution variable. I feel like I've tried every possible substitution, but … 
Alg2/Trig
Find the exact value of the trigonometric function given that sin u = 5/13 and cos v = 3/5. (Both u and v are in Quadrant II.) Find csc(uv). First of all, I drew the triangles of u and v. Also, I know the formula of sin(uv) is sin … 
Calculus
I need help with this integral. w= the integral from 0 to 5 24e^6t cos(2t) dt. i found the the integration in the integral table. (e^ax/a^2 + b^2) (a cos bx + b sin bx) im having trouble finishing the problem from here. 
Calculus
Hi there i am having some problems trying to do my calculus homework and i really need help on how to show the step to proof the volume of a sphere which is V= 4/3pirsquare. But I have to use triple integral to proof the volume of … 
calc
find integral using table of integrals ) integral sin^4xdx this the formula i used integral sin^n xdx =1/n sin^n1xcosx +n1/n integral sin^n2 using the formula this is what i got: integral sin^4xdx=1/4sin^3xcosx+3/4 integral sin^2xdx= … 
Calculus
Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral. 
Calculus
Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral, at the following … 
calculus
Integral csc^2 (2x+9)dx 
Trig verifying identities
I am having trouble with this problem. sec^2(pi/2x)1= cot ^2x I got : By cofunction identity sec(90 degrees  x) = csc x secx csc1 = cot^2x Then split sec x and csc1 into two fractions and multiplied both numerator and denominators …