Question

\(\Huge\int \frac {x^3}{(1+x^2)^3}\ dx\)
This........
p/s: no trigonometry here ...xD

Answer 1

\[u=1+x^2\implies x^2=u-1\implies du=2xdx\]so\[x^3dx=\frac12(u-1)du\]

Answer 2

so we get\[\int{\frac12(u-1)du\over u^3}=\frac12\int u^{-2}-u^{-3}du\]

Answer 3

if there is a specific part you don't understand please let me know

Answer 4

Wow nice substitution~

Answer 5

Someone else taught me that idea on OS, and now I pass it on :)
It's nice when the internet is doing something productive.