Question

Integrate this....

Answer 1

\[\frac{ x ^{5} }{ (x ^{2}+1)^{2} }\]

Answer 2

let u = x^2 + 1

Answer 3

http://integral-table.com/
choose the appropriate formula for your question from here

Answer 4

\[\frac{ x*( u -1 )^{2} }{ u ^{2} }*du*\frac{ dx }{ du }\]

You know what to do

do more exercises to know what formula you should choose

Answer 5

u substitution wouldn't really work here. I'm not entirely sure what you're doing either.

Answer 6

I know I need to integrate by parts, but I'm not sur how to set it up properly. I tried using long division, I couldn't figure it out.

Answer 7

\[\frac{x^5}{\left(x^2+1\right)^2}=-\frac{2 x}{x^2+1}+\frac{x}{\left(x^2+1\right)^2}+x \]

Answer 8

Thank you! I couldn't get the division right. I don't know why.

Answer 9

From Mathematica: "You're welcome"

Answer 10

Anyway you can work that out for me to see where I went wrong?

Answer 11

Refer to the solution for obtaining the partial fractions of interest, a modest problem in itself. Mathematica 8 Home Edition was used for the calculations.