Answer
\begin{aligned}
\int x^{2} \cosh x\ d x = x^2\sinh x-2x \cosh x+2 \sinh x+C\\
\end{aligned}
Work Step by Step
Given $$\int x^{2} \cosh x\ d x $$
So, we have
\begin{array}{|c c c|}\hline Differentiation && {Integration} \\
\hline
x^2 & + & \cosh x \\
&\searrow&\\ \hline
2x & - & \sinh x \\
&\searrow&\\ \hline
2 &+ & \cosh x \\
&\searrow&\\ \hline
0 & & \sinh x \\
&&\\ \hline
\end{array}
Therefore
\begin{aligned}
I&=\int x^{2} \cosh x\ d x\\
&= x^2\sinh x-2x \cosh x+2 \sinh x+C\\
\end{aligned}
