Question

integral of x^3//(1-x^2)
i got trig substitution to be me to the integral of sine thetea cubed. after that I would take one of the sines and convert. I would take sine to the second power. I changed this to 1-cos^2. Now I am stuck.
I have the integral of (1-cos^2x)/(sin^x). any input?

Answer 1

is your original Q this :
\(\int \dfrac{x^3}{\sqrt{1-x^2}}dx\)

Answer 2

if you put x= sin t there, you'd get
\(\int \sin^3 t \: dt\)
and you can use the sin 3x formula.
sin 3x = 3sin x -4 sin^3 x
isolate sin^3 x from here and substitute in your integral.

Answer 3

alternative :
we can solve by u subs ..
let u=1-x^2 ---> du = -2x dx or x dx = -du/2
x^2 = 1-u
so, ur integral can be :