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amorfide

  • 3 years ago

please someone tell me how to integrate sinh²xcoshx please please please please please please please please please please please

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  1. malevolence19
    • 3 years ago
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    \[\int\limits \sinh^2(x)\cosh(x)dx; \psi = \sinh(x) \implies d \psi = \cosh(x) dx \]\[\implies \int\limits \psi^2 d \psi = \frac{\sinh^3(x)}{3}+C\]

  2. amorfide
    • 3 years ago
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    I do not understand where the dividing by 3 came from

  3. malevolence19
    • 3 years ago
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    \[\int\limits \psi^2 d \psi = \frac{\psi^3}{3}+C; \psi = \sinh(x) \implies \frac{\sinh^3(x)}{3}+C\]

  4. amorfide
    • 3 years ago
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    that does not explain why we are dividing by 3

  5. malevolence19
    • 3 years ago
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    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
    • 3 years ago
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    for: \[n \in \mathbb{Z} \ne -1\]

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