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

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. calc help showed work

    If the function f has a continuous derivative on [0,c], the the integral(o to c) of f'(x)dx= a)f(c)-f(0) b)absolute value (f(c)- f(0)) c) f(c) d)f'(x)=c e)f"(c)-f"(0) My work: so the the answer to the integral is f(x) and when

  2. 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

  3. English

    1. I am into sports. (What is the meaning of this sentence?) 2. Exercise is good for the health. 2-1. Exercise is good for health. 2-2. Exercise is good for your health. 2-3. Exercise does good for people. (Are all correct?) 3.

  4. Calculus

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a

  1. Math:)

    1. Simplify the expression. [csc^2(x-1)]/[1+sin x] a. csc x+1 b. csc x(csc x-1) c. sin^2 x-csc x**** d. csc^2 x-cos xtan x 2. Which of the following expressions can be used to complete the equation below? sec x/1+cot^2 x a. tan x

  2. Quick calc question

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is false? the integral from a to b of the sum of f of x and g of x, dx equals the integral from a to b of f of x, dx plus the integral from a to b of

  3. Trignometry

    Use the appropriate reciprocal identity to find the approximate value of sin θ for the given value of csc θ. Use a calculator. csc θ = 2.15750581

  4. Calculus

    Which of the following integrals can be integrated using partial fractions using linear factors with real coefficients? a) integral 1/(x^4-1) dx b) integral (3x+1)/(x^2+6x+8) dx c) integral x^2/(x^2+4) d) None of these

  1. Math (Precal)

    csc^2x secx/sec^2x+csc^2x simplify.

  2. Precalculus

    Having trouble with this: Verify: csc^4x-cot^4x=2csc^2x-1 *the numbers after the carets are to the power of

  3. Physics, Calculus(alot of stuff together)= HELP!!

    A rod extending between x=0 and x= 14.0cm has a uniform cross- sectional area A= 9.00cm^2. It is made from a continuously changing alloy of metals so that along it's length it's density changes steadily from 2.70g/cm^3 to

  4. Math

    How to prove this question with using a LS=RS-style Proof? csc^2(x)cos^2(x) = csc^2(x)-1

You can view more similar questions or ask a new question.