Calculus

posted by .

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

First Name
School Subject
Your Answer

Similar Questions

  1. 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; …
  2. 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 …
  3. 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(u-v). First of all, I drew the triangles of u and v. Also, I know the formula of sin(u-v) is sin …
  4. 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.
  5. 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 …
  6. calc

    find integral using table of integrals ) integral sin^4xdx this the formula i used integral sin^n xdx =-1/n sin^n-1xcosx +n-1/n integral sin^n-2 using the formula this is what i got: integral sin^4xdx=-1/4sin^3xcosx+3/4 integral sin^2xdx= …
  7. 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.
  8. 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 …
  9. calculus

    Integral -csc^2 (2x+9)dx
  10. Trig verifying identities

    I am having trouble with this problem. sec^2(pi/2-x)-1= cot ^2x I got : By cofunction identity sec(90 degrees - x) = csc x secx csc-1 = cot^2x Then split sec x and csc-1 into two fractions and multiplied both numerator and denominators …

More Similar Questions