Question

how would you integrate x^3 / sqrt(1 - x^2 )

Answer 1

I think everyone is asleep.

Answer 2

This is a non-elementary integral. D:

Answer 3

I have found sqrt(1 - x^3 - sqrt(1 - x^2 )/ 3 not sure if its correct ,I think there was a way to check your answer using wolfram or something

Answer 4

interesting. try differentiating it maybe?

Answer 5

as far as I know, this shouldn't have a simple form.

Answer 6

what methods have you learned so far

Answer 7

you there?

Answer 8

ye

Answer 9

\[I=\int\limits \frac{ x^3 }{ \sqrt{1-x^2} }dx\]

put \[\sqrt{1-x^2}=t,x^2=1-t^2,2x dx=-2t dt\]
\[=\int\limits \frac{ x^2 x dx }{ \sqrt{1-x^2} }=\int\limits \frac{ \left( 1-t^2 \right)\left( -t dt \right) }{ t }=-\int\limits \left( 1-t^2 \right)dt\]
=?

Answer 10

i think now you can complete.

Answer 11

you got it or any doubt.