Question

please someone tell me how to integrate
sinh²xcoshx

please please please please please please please please please please please

Answer 1

\[\int\limits \sinh^2(x)\cosh(x)dx; \psi = \sinh(x) \implies d \psi = \cosh(x) dx \]\[\implies \int\limits \psi^2 d \psi = \frac{\sinh^3(x)}{3}+C\]

Answer 2

I do not understand where the dividing by 3 came from

Answer 3

\[\int\limits \psi^2 d \psi = \frac{\psi^3}{3}+C; \psi = \sinh(x) \implies \frac{\sinh^3(x)}{3}+C\]

Answer 4

that does not explain why we are dividing by 3

Answer 5

Its the integral of psi^2...
\[\int\limits x^n dx = \frac{x^{n+1}}{n+1}; n=2 \implies \int\limits x^2 dx = \frac{x^{2+1}}{2+1}= \frac{x^3}{3}\]

Answer 6

for:
\[n \in \mathbb{Z} \ne -1\]