Question

Integrate the following function $\sin h^{2}x$ with respect to $x$.

Answer 1

$sinhx=\frac{e^x-e^{-x}}{2}$

$sin{h}^{2}x=\frac{e^{2x}++e^{-2x}-2}{4}$

$\Rightarrow \int sin{h}^2\left(x\right)dx=\int \frac{1}{4}(e^{2x}+e^{-2x}-2)dx$

$\Rightarrow \frac{1}{8}{e}^{2x}-\frac{1}{8}{e}^{-2x}-\frac{x}{2}+constant$