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There is one other tool that can sometimes be used to evaluate
anti-derivatives that works when certain convergence conditions
hold. Suppose we know the anti-derivative of g(x,a) where
g is some differentiable function of the parameter a, as well
as a function of x. Then we can deduce that an anti-derivative
of 
is the derivative with respect to a of an anti-derivative
of g.
For example, we know that an anti-derivative of 
We may then deduce that an anti-derivative of  ,
and we can take higher derivatives with respect to a here
as well. This gives us a formula for an anti-derivative of
a function of the form xk eax, as
If you cannot stand the idea of differentiating
with respect to a, change a to y wherever it appears, and
replace the derivative with respect to a by the partial derivative
with respect to y. Then smile.
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