U substitution for integral of cos(π/x¹¹)/x¹²

[miller8605]

I don't have a way of getting the equation to look nice but it's:

integral of cos(pi/x^11) / x^12




I am having issues even finding what I could use as a U substitution. Any help would be great!

 

[rootX]

Thing causing trouble is cos(pi/x^11) / x^12

 

[Dick]

How about u=pi/x^11?

 

[miller8605]

How about u=pi/x^11?

problem with that is when you take the derivative, you don't have the dx int he problem.

i'm almost certain the U has to equal x^12 as then du would then be 11x^11 and you can divide that by 11 and stick a 1/11 out front. I just don't know how to get du out of that stupid fraction. unless I'm going about it completely wrong and it's not a U substitution and it's a by parts question.

 

[Dick]

If u=pi/x^11 then what do you think is du?

 

[miller8605]

(-11pi*x^10) / x^11

if I used the quotient rule correctly

 

[Dick]

You forgot to square the denominator.

 

[miller8605]

You forgot to square the denominator.

it looks like i did, i forgot the derivate of pi was zero, haha. dumb on my part.

but that doesn't get me anywhere because no where in the original problem is the du. i have to get rid of that 1/x^12 somehow.

 

[Dick]

Simplify (-11pi*x^10) / (x^11)^2.

 

[miller8605]

Simplify (-11pi*x^10) / (x^11)^2.

wow, can't believe i missed that. thanks for all your help, i'll post up my answer here in a couple minutes.

 

[miller8605]

-1/11pi * sin(pi/x^11) + C

 

[Dick]

Looks ok to me.