Solve. integration of (1+v^2) /(1-v^3)

So,



The first integral is easy. For the second, since the derivative of the denominator is , we can add and subtract to get



and for the first term employ a substitution. For the remaining term, we can complete the square in the denominator, then use a trigonometric substitution:



where , and



Then taking gives





Now we're ready to wrap up.








This can be simplified a bit using some properties of logarithms to obtain