`int (arcsin(x))^2 dx` Evaluate the integral

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You need to use integration by parts, such that:

 

`int udv = uv - int v du`

`u = (arcsin^2(x))=> du = (2arcsin x)/(sqrt(1-x^2))dx`

`dv = 1 => v = x`

`int (arcsin^2(x)) dx = x*(arcsin^2(x)) - 2 int arcsin x*x/(sqrt(1-x^2))dx`

You need to solve the integral `int arcsin x*(x/(sqrt(1-x^2)))dx` using substitution `arcsin x= t` , such that:

`arcsin...

(The entire section contains 209 words.)

Unlock This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial
Approved by eNotes Editorial Team