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Homework Statement
\int\frac{x^3}{\sqrt{1-x^2}}dx
I have to use integration by parts on the above integral.
Homework Equations
The Attempt at a Solution
u=x^3
du=3x^2dx
dv=\frac{1}{\sqrt{1-x^2}}dx
v=arcsin (x)
=x^3arcsin (x)-3\int\ x^2arcsin (x)dx
u=arcsin (x)
du=\frac{1}{\sqrt{1-x^2}}dx
dv=x^2dx
v=\frac{1}{3}x^3
\int\frac{x^3}{\sqrt{1-x^2}}dx==x^3arcsin (x)-3[x^2 arcsin(x)-\frac{1}{3} \int\ \frac{x^3}{\sqrt{1-x^2}} dx
\int\frac{x^3}{\sqrt{1-x^2}}dx=x^3arcsin (x)-3x^2 arcsin(x) + \int\ \frac{x^3}{\sqrt{1-x^2}} dx
Here I was hoping I could move the integral over but, given the signs, that isn't going to work. Any tips on what course I should take instead?