Question

What is the antiderivative of `x/(x^2 + 4)`?

Answer 1

`int (xdx)/(x^2+4) = 1/2ln(x^2+4) + C`

Explanation:

Substitute `t=x^2+4`, `dt=2xdx`, so that:

`int (xdx)/(x^2+4) = 1/2 int dt/t = 1/2lnabst + C`

and undoing the substitution:

`int (xdx)/(x^2+4) = 1/2ln(x^2+4) + C`