## appleduardo 3 years ago whats the integral of arc sin x ??

1. appleduardo

so far i have:$x(arcsinx)-\int\limits_{}^{}x \frac{ 1 }{ \sqrt{1-x^2} }dx$

2. Kainui

Looks like you've done most of the hard part. Now take 1-x^2 and integrate by subtitution.

3. appleduardo

uhmm how can i do that?

4. appleduardo

there's where i got confused!

5. dumbcow

trig substitution x = sin(u) dx = cos(u) du

6. Kainui

So take (1-x^2)=u and take the derivative with respect to x, this becomes -2x=du/dx which can be rearranged with algebra into: xdx=-(1/2)du Substitution back into the original integrand gives: $-\int\limits_{}^{}\frac{- du }{ 2\sqrt{u} } = \frac{ 1 }{ 2 }\int\limits_{}^{}\ u^{-1/2} du$

7. Kainui

@dumbcow trig substitution isn't really useful here.