Homework Help: Evaluate this integral

1. Jan 20, 2008

Vash

1. The problem statement, all variables and given/known data

elvaluate this integral (arcsinx)^2dx

2. Relevant equations

(arcsinx)^2dx

3. The attempt at a solution

integration by parts, let u= arcsinx and make y=arcsinx for easier integration. Once i plug it into the parts equation it turns into a mess. Any help would be superb.

2. Jan 20, 2008

G01

This should be solvable by using substitution and integration by parts one after the other.

HINT: Let sin u = x.

3. Jan 20, 2008

Vash

That's what I've been doing and it still doesn't work out for me....oh well, I'll keep trying.

4. Jan 20, 2008

rocomath

$$\int(\sin^{-1}x)^2dx$$

$$t=\sin^{-1}x$$
$$dt=\frac{dx}{\sqrt{1-x^2}}$$

$$x=\sin t$$
$$dt=\frac{dx}{\sqrt{1-\sin^2 t}}$$

Continue simplifying and see what you can get.

Last edited: Jan 20, 2008
5. Jan 20, 2008

Vash

im getting xarcsinx+sqrt(1-x^2)

6. Jan 20, 2008

rocomath

Final answer? Take the derivative and see if you get your Integral.

7. Jan 20, 2008

Vash

Im not sure how to do it your way so I just set it up by integration by parts. u=arcsinx, du=1/(sqrt(1-x^2)) dv=dx v=x. When I do it i get my answer above.

8. Jan 20, 2008

rocomath

After simplifying, the Integral becomes ...

$$\int t^2 \cos t dt$$

Last edited: Jan 20, 2008