Integral of $\cosh^3(x)$ What is the integral of $\cosh^3(x)$? And how exactly can I calculate it? I've tried setting $\cosh^3(x)=(\frac{e^x+e^{-x}}{2})^3$ but all I get in the end is one long fraction.
Hint: $\cosh^3x=\cosh x\cdot\cosh^2x=\sinh'x\cdot\big(1+\sinh^2x\big)$.
\begin{align}
\int\cosh^3x dx &amp; = \int\left(\sinh^2x +1\right)\cosh x dx \\
&amp; = \frac{1}{3}\int3\sinh^2x\cosh x dx +\int \cosh x dx \\
&amp; = \frac{1}{3}\sinh^3 x + \sinh x + C\\
\end{align}