# Primitive of Square of Hyperbolic Cosine Function/Corollary

## Corollary to Primitive of Square of Hyperbolic Cosine Function

$\displaystyle \int \cosh^2 x \rd x = \frac {\sinh x \cosh x + x} 2 + C$

where $C$ is an arbitrary constant.

## Proof

 $\displaystyle \int \cosh^2 x \rd x$ $=$ $\displaystyle \frac {\sinh 2 x} 4 + \frac x 2 + C$ Primitive of Square of Hyperbolic Cosine Function $\displaystyle$ $=$ $\displaystyle \frac {2 \sinh x \cosh x} 4 + \frac x 2 + C$ Double Angle Formula for Hyperbolic Sine $\displaystyle$ $=$ $\displaystyle \frac {\sinh x \cosh x + x} 2 + C$ rearranging

$\blacksquare$