Thread: integration

Can someone help me with this equation please Sinh^5x coshx dx thanks.

Originally Posted by Link88

Can someone help me with this equation please Sinh^5x coshx dx thanks.

$\displaystyle \int \sinh^{5}(x) \cosh(x) dx$
Let's use u-Substitution.

$\displaystyle u = \sinh(x)$
$\displaystyle du = \cosh(x) dx$
So, using these in our original integral and it's pretty simple from here.

$\displaystyle \int u^5 du = \frac {u^6}{6}+C$
Subbing back in u = sinh(x) and you get

$\displaystyle =\frac {\sinh^{6}(x)}{6}+C$