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Thread: Which identity is used here?

  1. #1
    Senior Member Vinod's Avatar
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    Which identity is used here?

    Hello,
    When I solved $\int e^{2x}*\cosh(x)dx$, I got the answer $(\frac{-\sinh(x)}{3}+\frac23\cosh(x))*e^{2x}+C$. But the answer provided is $\frac{e^{3x}}{6}+\frac{e^x}{2}+C$.Both answers are equal. I want to know which identity is used for making both of them equivalent?
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  2. #2
    MHF Contributor
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    Re: Which identity is used here?

    No identities. Just definitions.

    $$\sinh x \stackrel{\text{def}}{=} \dfrac{e^x-e^{-x}}{2}$$

    $$\cosh x \stackrel{\text{def}}{=} \dfrac{e^x+e^{-x}}{2}$$
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