Setting up our partial fractions we get

Multiplying through by

we get

Grouping we get

Equating Coefficients we first get

Next we have that

Next we have

And finally

Putting it back into our original we get

So now

The first integral is a arctangent so

Noticing in the second one that x is 1/2 the derivative of the quantity

we rewrite to get

Combining we get