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# integral of ((sinh(x))^9)cosh(x) ? Watch

1. Problem solved, no more help needed.

as title says - i dont know how to start with integrating ((sinh(x))^9)cosh(x)

am i missing a key formula? (im not very good with hyperbolic trig functions)

any help appreciated + rep
2. (Original post by Lewk)
as title says - i dont know how to start with integrating ((sinh(x))^9)cosh(x)

am i missing a key formula? (im not very good with hyperbolic trig functions)

any help appreciated + rep
My initial thoughts would be to use the substitution u=sinhx.
3. (Original post by ttoby)
My initial thoughts would be to use the substitution u=sinhx.
^^ This. If you do this the solution comes out very quickly.
4. (Original post by ttoby)
My initial thoughts would be to use the substitution u=sinhx.
This is correct. A dx might be useful to the OP too.
5. Or you might want to consider what happens when you differentiate .
6. (Original post by ttoby)
My initial thoughts would be to use the substitution u=sinhx.
lol that was very straight forward thanks, it just 'looks' hard
7. i'd consider the reduction formula

Spoiler:
Show
nah not really, i'd just do what marcus said
8. (Original post by Lewk)
lol that was very straight forward thanks, it just 'looks' hard
If you see something that looks hard, try to spot tricks. Here, we have a function of a function (that is, which is multiplied by the derivative of the inner function.

So for example if you saw then you'd probably panic, but when you notice that is the derivative of you can deduce that the substitution will give you , which is much easier to get your head around!

Other such things to look for are:
- partial fractions
- things you can use integration by parts on
- things in the form , which simply integrate to

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