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    how do i integrate the following:

    a) sin(sin(x))
    b) x cos(cos(x))
    c) ((|x|)^m)/(x^n) for m>n
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    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.
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    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.
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    (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.
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    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?)
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    I can't integrate that either...
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    Well, I don't fancy trying it, but at least there's a method for doing so.
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    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.
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    If the computers can't do it, I'm glad I didn't waste time trying.

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

    Which was the first suggestion given.....
 
 
 

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