Problem: Evaluate the integral with parameter

Solution: This integral clearly fits into the box integration by parts, namely it is the type "removing powers". We therefore apply the appropriate method.

The integral for g is elementary, just a simple linear substitution, and we do not let the parameter bother us.

An experienced integrator would do it right ahead in his head. However, we have a problem here, what if a = 0? We leave it for later, now we conclude our calculations assuming that a is well-behaved.

Now we check on the case a = 0. That is no problem, we simply put this a into the given integral aand see what we have there.

That was really simple. Now we put it together.

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