How can I intagrate this problem by substitution?

[Zame]

[MATH]\int \:\frac{x^4}{\left(x^2+1\right)^2}dx[/MATH]

 

[Deleted member 4993]

[MATH]\int \:\frac{x^4}{\left(x^2+1\right)^2}dx[/MATH]

substitute:

x = tan(u)

 

[Zame]

substitute:

x = tan(u)

I did that but then i dont know what to do after [MATH]\int \:\frac{\tan ^4\left(u\right)}{\sec ^2\left(u\right)}du[/MATH]

 

[Deleted member 4993]

I did that but then i dont know what to do after [MATH]\int \:\frac{\tan ^4\left(u\right)}{\sec ^2\left(u\right)}du[/MATH]

\(\displaystyle \frac{tan^4(u)}{sec^2(u)}\)

=\(\displaystyle tan^2(u) * sin^2(u)\)

= \(\displaystyle tan^2(u) * [1- cos^2(u)] \)

= \(\displaystyle tan^2(u) - sin^2(u) \)

continue.....