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

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appleduardo
 3 years ago
Best ResponseYou've already chosen the best response.0so far i have:\[x(arcsinx)\int\limits_{}^{}x \frac{ 1 }{ \sqrt{1x^2} }dx\]

Kainui
 3 years ago
Best ResponseYou've already chosen the best response.2Looks like you've done most of the hard part. Now take 1x^2 and integrate by subtitution.

appleduardo
 3 years ago
Best ResponseYou've already chosen the best response.0uhmm how can i do that?

appleduardo
 3 years ago
Best ResponseYou've already chosen the best response.0there's where i got confused!

dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.0trig substitution x = sin(u) dx = cos(u) du

Kainui
 3 years ago
Best ResponseYou've already chosen the best response.2So take (1x^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: \[\int\limits_{}^{}\frac{ du }{ 2\sqrt{u} } = \frac{ 1 }{ 2 }\int\limits_{}^{}\ u^{1/2} du\]

Kainui
 3 years ago
Best ResponseYou've already chosen the best response.2@dumbcow trig substitution isn't really useful here.
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