Almost anytime you have x, or a power of x, multiplied by another function of x, you should think "integration by parts". If you let u= x, then du= dx so you have gotten rid of that x (if you have a power of x, setting u equal to that power of x reduces the power and repeated integration by parts will eliminate it altogether).
Of course, now dv= tan(x)dx. Do you know the anti-derivative of tan(x)?
If not, think of it as and use the substitution u= cos(x).
So by integration by parts, we have:
At this point, I recall that one of the definitions of Catalan's constant was
So I write
Thus