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\noindent This is a variant of the problem w2D. It is intended to be used right before problem esergel55.

\begin{questions}


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\question % based on workshop bank Ch. 5 -> w2D

\begin{parts}

\part There are values of the constants $A$ and $B$ so that the derivative of $Axe^x + Be^x$ is $xe^x$. Find these values.
% [ xe^x - e^x ]' = [ xe^x + e^x - e^x ] = xe^x
% A=1, B=-1

\part Use your answer from part (a) to compute $\int_1^2 xe^x \, dx$.
% [ (x-1)e^x ]_1^2 = e^2 - 0 = e^2

\part Compute the derivative of $x\ln(x)$.
% [ x\ln(x) ]' = \ln(x) + 1

\part Find the general antiderivative of $\ln(x)$.
% x\ln(x) - x + C

\end{parts}

\end{questions}

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