The Student Room Group
Reply 1
Notice that coshx is the derivative of sinhx so you have:
f'(x) * f(x)^2

What's the integral of something of this form?
Reply 2
can u write the full answer plz!
f40spider
can u write the full answer plz!

Try differentiating sinh3x \sinh ^3 x by the chain rule.
You should get something that looks similar to what you're trying to integrate. You can make it exact by multiplying by a constant (constants do not affect differentiation/integration).
For the purposes of this you can think of integration as reverse differentiation, for example if you differentiate x^2 you get 2x and if you integrate 2x you get x^2.

This is how I always do these problems, it also works if you have to integrate something like sinxcosnx \sin x \cos ^n x , if you differentiate cosn+1x \cos ^{n+1} x you'll get something in a similar form.

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