Possible Integration by Parts Exam Practice Problems

Goldenwind
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Homework Statement


Got an exam later today on this, just looking for some practice.
I know this is kinda reverse of what the forum is intended for, but I'd like to ask for people to post some problems that I can solve via Integration by Parts.

Just like 5 or so.

Homework Equations


Integral(u dv) = uv - Integral(v du)
 
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\int\frac{r^3}{\sqrt{4+r^2}}dx

\int\ln \sqrt{1+x^2}dx

\int\sec^{3}xdx

\int\sec^{5}xdx

\int x\tan^{-1}xdx
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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