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# Integrating cosh^3(x) Tweet

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1. Integrating cosh^3(x)
Hi. The question is to integrate cosh^3(x) and I managed to get the following answer: sinhx + 1/3sinh^3(x) + C however the answer in the book and the answer that Wolfram Alpha is getting is 1/12(9sinh(x) + sinh(3x)).

I just can't think of any identity to turn my answer into the one in the book.

Thank you!
2. Re: Integrating cosh^3(x)

= 1/2(e^x-e^-x)+ 1/24(-e^-3x + 3e^-x -3e^x + e^3x)
= 1/2(e^x)-1/2(e^-x) +1/8(e^-x) -1/8(e^x) -1/24(e^-3x) + 1/24(e^3x)
=3/8(e^x-e^-x)+1/24(e^3x-e^-3x)
= 3/4(1/2(e^x-e^-x)+ 1/12(1/2(e^3x-e^-3x)
= 3/4sinhx + 1/12sinh3x
= 1/12(9sinhx+ sinh3x)
3. Re: Integrating cosh^3(x)
(Original post by Shaare)
Hi. The question is to integrate cosh^3(x) and I managed to get the following answer: sinhx + 1/3sinh^3(x) + C however the answer in the book and the answer that Wolfram Alpha is getting is 1/12(9sinh(x) + sinh(3x)).

I just can't think of any identity to turn my answer into the one in the book.

Thank you!

So
4. Re: Integrating cosh^3(x)
Got it. Thank you for your replies!