Question

Integrate xdx/x^2+a^2=?

Answer 1

`intx/(x^2+a^2)dx=1/2ln|x^2+a^2|+C`

Explanation:

Let `u(x)=x^2+a^2"` then `du=2xdx` or `xdx=(du)/2`

and `intx/(x^2+a^2)dx`

= `int(du)/(2u)`

= `1/2int(du)/u`

= `1/2ln|u|+C`

= `1/2ln|x^2+a^2|+C`