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This is the only question in my homework that I can't finish. I'm having issues with taking the integral of the function. I have set $e^{x}$ as the u for substitution and also $sinh(x)+cosh(x)$, too but nothing worked.

$\int_{-12}^{12} \frac{3e^{x}}{\sinh(x)+\cosh(x)}dx$

binibiningtinamoran
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  • Substitute $u=e^x$ and use that $\sinh x=\frac{1}{2}\left(e^x-e^{-x}\right)$ and $\cosh x=\frac{1}{2}\left(e^x+e^{-x}\right)$. – RMWGNE96 May 10 '19 at 07:58
  • Recall that their definitions are $\cosh(x)=\frac{e^x+e^{-x}}{2}$ and $\sinh(x)=\frac{e^x-e^{-x}}{2}$ – logarithm May 10 '19 at 07:59
  • Oh wait, the final answer should be $72$ then. Things cancel in a funny way. – RMWGNE96 May 10 '19 at 08:00
  • If you solved it, for the sake of posterity, writing a short answer explaining what you did to solve it and accepting it would be a good thing. – Arthur May 10 '19 at 08:00

1 Answers1

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As pointed out in the comments, we have $\sinh x+\cosh x=e^x$. The integrand then is $3$, so the final answer is $3\cdot(12-(-12))=72$.

RMWGNE96
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