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  1. #1
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    pls help to find integral

    I have two questions. My idea was to use u substitution or integration by partspls help to find integral-101.png

    pls help to find integral-120.pngi would appreciate the help.
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  2. #2
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    Re: pls help to find integral

    here has a form identical to your second integral.

    It's recursive though. You'll need to write a small program to evaluate it.

    For your first integral there's nothing fundamentally tricky about it. You can use binomial expansion to deal with the second term and then just multiply by the first. Each of the summands is easily integrated. Again a short program will take care of keeping track of all the terms.

    There may be some super clever trick here I don't know about.
    Last edited by romsek; February 23rd 2014 at 11:35 AM.
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  3. #3
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    Re: pls help to find integral

    Quote Originally Posted by start5 View Post
    I have two questions. My idea was to use u substitution or integration by partsClick image for larger version. 

Name:	101.png 
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    Click image for larger version. 

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ID:	30229i would appreciate the help.
    $\displaystyle\int {{{\sin }^{76}}(x){{\cos }^3}(x)dx = \int {{{\sin }^{76}}(x)\cos (x)dx} } - \int {{{\sin }^{78}}(x)\cos (x)dx} $
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  4. #4
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    Re: pls help to find integral

    For the first one, substitute u = 1 + x^2 + x^4. Then du = (2x + 4x^3)\,dx, which is just half of the first polynomial 4x + 8x^3.

    - Hollywood
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  5. #5
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    Re: pls help to find integral

    oh well the trig integral becomes simple then as well.

    let

    $$u=sin(x)$$
    $$du=cos(x)dx$$
    Last edited by romsek; February 23rd 2014 at 06:09 PM.
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    Re: pls help to find integral

    Quote Originally Posted by romsek View Post
    oh well the trig integral becomes simple then as well.
    let $$u=sin(x)$$ $$du=cos(x)dx$$
    $$cos^2(x)=1-sin^2(x)$$
    $$\int \left(u^{76}-u^{78}\right)du=\frac{u^{77}}{77}-\frac{u^{79}}{79}=$$
    $$\frac{\sin^{77}(x)}{77}-\frac{\sin^{79}(x)}{79}$$
    Why are we now giving out giving out complete solutions?
    Last edited by Plato; February 23rd 2014 at 06:04 PM.
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  7. #7
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    Re: pls help to find integral

    fixed

    of course the solution is in your quote and there's nothing I can do about that.
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