(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int\frac{x^3}{\sqrt{1-x^2}}dx[/tex]

I have to use integration by parts on the above integral.

2. Relevant equations

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integration by Parts problem

**Physics Forums | Science Articles, Homework Help, Discussion**