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Homework Statement
[tex]\int\frac{x^3}{\sqrt{1-x^2}}dx[/tex]
I have to use integration by parts on the above integral.
Homework Equations
The Attempt at a Solution
[tex]u=x^3[/tex]
[tex]du=3x^2dx[/tex]
[tex]dv=\frac{1}{\sqrt{1-x^2}}dx[/tex]
[tex]v=arcsin (x)[/tex]
[tex]=x^3arcsin (x)-3\int\ x^2arcsin (x)dx[/tex]
[tex]u=arcsin (x)[/tex]
[tex]du=\frac{1}{\sqrt{1-x^2}}dx[/tex]
[tex]dv=x^2dx[/tex]
[tex]v=\frac{1}{3}x^3[/tex]
[tex]\int\frac{x^3}{\sqrt{1-x^2}}dx[/tex]=[tex]=x^3arcsin (x)-3[x^2 arcsin(x)-\frac{1}{3} \int\ \frac{x^3}{\sqrt{1-x^2}} dx[/tex]
[tex]\int\frac{x^3}{\sqrt{1-x^2}}dx[/tex][tex]=x^3arcsin (x)-3x^2 arcsin(x) + \int\ \frac{x^3}{\sqrt{1-x^2}} dx[/tex]
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?