Question

Integrate the following functions with respect to $x$:
(a) $\sinh 4x$
(b) ${\cosh }^{2}3x$

Answer 1

$\left(a\right)\int \sinh \left(4x\right)dx=\int \frac{e^{4x}-e^{-4x}}{2}dx$

$=\frac{1}{2}(\frac{e^{4x}}{4}-\frac{e^{-4x}}{-4})$

$=\frac{e^{4x}}{8}+\frac{e^{-4x}}{8}$

$\left(b\right)\int \cos h^2\left(3x\right)dx=\int \frac{e^{6x}+e^{-6x}+2}{2}dx$

$=\frac{1}{2}(\frac{e^{6x}}{6}+\frac{e^{-6x}}{-6}+2x)$

$=\frac{1}{6}\left(\sinh 6x\right)+x$