Math, asked by MissTanya, 11 months ago

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Can anyone solve this for me...
My question is
Int (sinh^2x+cosh^2x) dx
I want step by step solution...
So please NO SPAMMING
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Answers

Answered by SirSumit

This may help you bro..good luck!

Attachments:

MissTanya: thanks bro...

MissTanya: It has some mistakes but helps me a lot...

MissTanya: sorry i have to report that solution...

MissTanya: Becoz other users might get disturbed while finding their solutions...

SirSumit: ok no problem

MissTanya: By the way i m sis not bro...

SirSumit: ok sis

SirSumit: i called you bro as per your name

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Answered by Anonymous

Answer:

always prefer to do a u-substitution rather than integration by parts. As an analogy to circular trig functions,

sin(2x)=2sinxcosx

and it can be shown that

sinh(2x)=2sinhxcoshx

Using this identity, rewrite the integral to get:

∫sinh(2x)cosh(x)dx=∫2sinh(x)cosh(x)cosh(x)dx=2∫sinh(x)cosh2(x)dx

Now is the time for a u-substitution where we let u=cosh(x), and then du=sinh(x)dx. Thus,

2∫sinh(x)cosh2(x)dx=2∫u2du=2(u33)+C

Back-substituting in the value of u gives your final answer

23cosh3(x)+C

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