$\int {sinh}^{2} (x) cosh (x) d x$ $\int\sinh^2(x)\cosh(x)dx$ ?

Question

Mostly not sure what to use for u-substitution. :\

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Answer 1 · 2017-09-17T16:48:21

see below

If the question was meant to be $I = \int {sinh}^{2} x cosh x d x$ $I=intsinh^2xcoshxdx$

by inspection the answer would be

$\frac{1}{3} {sinh}^{3} x + C$ $1/3sinh^3x+C$

by substitution

$u = sinh x \Rightarrow d u = cosh x d x$ $u=sinhx=>du=coshxdx$

$I=intu^2cancel(coshu)xx(du)/cancel(coshu)$

$=intu^2du=1/3u^3+C$

$=1/3sinh^3x+C$