Question

Integrate the following with respect to $x$.
$\cos h3x$

Answer 1

$\int \cos h3xdx$ = $\int \frac{e^{3x}+e^{-3x}}{2}dx$

$\int \cos h3xdx$ = $\frac{1}{2}(\int e^{3x}dx+\int e^{-3x}dx)$

$\int \cos h3xdx$ = $\frac{1}{2}\left(\frac{e^{3x}-e^{-3x}}{3}\right)$

now, $\sin h3x=\frac{e^{3x}-e^{-3x}}{2}$

then ,

$\int \cos h3xdx$ = $\frac{1}{3}\sin h3x+constant$