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## amorfide Group Title please someone tell me how to integrate sinh²xcoshx please please please please please please please please please please please one year ago one year ago

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1. malevolence19 Group Title

$\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$

2. amorfide Group Title

I do not understand where the dividing by 3 came from

3. malevolence19 Group Title

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

4. amorfide Group Title

that does not explain why we are dividing by 3

5. malevolence19 Group Title

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

6. malevolence19 Group Title

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