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- Jan 27th 2011, 07:16 AMjacksdefinite integral
- Jan 27th 2011, 07:23 AMHallsofIvy
**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). - Jan 27th 2011, 07:30 AMProve It
- Jan 27th 2011, 09:38 AMTheCoffeeMachine
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