Add solution to problem

Author: dlglin

OpenProblemLibrary/Union/setIntByParts/sc5_6_01.pg

@@ -35,4 +35,19 @@ Evaluate the indefinite integral.
 [_]{$antideriv->cmp(upToConstant=>1)}{50} [` + C`].
 END_PGML
 
+BEGIN_PGML_SOLUTION
+Calculate the integral using integration by parts.
+
+Let [`u=x`] and [`dv=e^{[$a]x}dx`]
+
+Then [`du=dx`] and [`v=\frac{1}{[$a]}e^{[$a]x}`].
+
+[``\int u\,dv=uv-\int v\,du``], so
+
+[``\begin{eqnarray}\int xe^{[$a]x}\,dx & = & x\left(\frac{1}{[$a]}e^{[$a]x}\right)-\int \frac{1}{[$a]}e^{[$a]x}\,dx\\
+& = & \frac{1}{[$a]}\left(xe^{[$a]x}-\int e^[$a]x\,dx\right)+C\\
+& = & \frac{1}{[$a]}\left(xe^{[$a]x}-\frac{1}{[$a]} e^[$a]x\,dx\right)+C
+\end{eqnarray}``]
+END_PGML_SOLUTION
+
 ENDDOCUMENT();