Inverse Differential Operator ..

__Problem:__

Evaluate $\displaystyle e^x \; \dfrac{1}{D(D-1)} \; x$

__Solution:__

I have two ways here:

First Way: integrate x then calculate 1/(D-1) for the result (wich is x^2/2)

Second Way: evaluate 1/(D-1) for x then integrate the result

The problem here is that the two ways gives different results!

first way gives: $\displaystyle -e^x (\dfrac{1}{2}x^2+x+1)$

second way gives: $\displaystyle -e^x(\dfrac{1}{2}x^2+x)$

What's wrong?

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Anyone know a good site contains practice problems in inverse differential operator??