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# Integration difficulies watch

1. how do i integrate the following:

a) sin(sin(x))
b) x cos(cos(x))
c) ((|x|)^m)/(x^n) for m>n
2. Use a subsitution of u = sin x

y = sin u, u = sin x
dy/du = cos u, du/dx = cos x
dy/dx = cos u cos x = cos(sin x) cos x

I think, never done one of those before.
3. That looks to me like differentiation. Maple can't do it so I have a feeling it's not traightforward, if it is indeed integrable.
4. (Original post by jamesgurung)
That looks to me like differentiation. Maple can't do it so I have a feeling it's not traightforward, if it is indeed integrable.
Damn. Can't read. Never mind. No idea how to integrate though.
5. it's ages since I did this, so I may be way off, but can you try

substituting u = sinx so du = cos x dx so dx = du/cos x

Then y = sin u

Int sin u dx = Int sin u du /(cos x)

That gives you x still, on the bottom but since cos^2 x = 1 - sin ^2 x = 1 - u^2, then cos x = (1 - u^2) ^0.5

Then can you integrate it by parts ? You'd be integrating

sin u / (1 - u^2) ^0.5 du ????

(Do I mean integration by parts? to integrate the fraction?)
6. I can't integrate that either...
7. Well, I don't fancy trying it, but at least there's a method for doing so.
8. If The Integrator and Maple (mentioned above) can't do it, it can't be done. Your "method" is useless.

A note for the third one: You can integrate for x >= 0. You can integrate for x <= 0. But you can't integrate for both in one expression.
9. If the computers can't do it, I'm glad I didn't waste time trying.

Are those questions definitely correct?
10. I think he meant differentiation
11. Oh &*@!

Which was the first suggestion given.....

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