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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
3
This may help you bro..good luck!
Attachments:
MissTanya:
thanks bro...
It has some mistakes but helps me a lot...
sorry i have to report that solution...
Becoz other users might get disturbed while finding their solutions...
ok no problem
By the way i m sis not bro...
ok sis
i called you bro as per your name
Ohh...
^_^
Answered by
5
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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