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Math Help - [SOLVED] ∫ xcos^2(2x)dx & ∫ln(x^2+14x+49)dx

  1. #1
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    [SOLVED] ∫ xcos^2(2x)dx & ∫ln(x^2+14x+49)dx

    Hi,
    I would like some help evaluating the following integrals.
    I'm not sure if I am doing all the right steps.


    xcos^{2}(2x)dx

    ln(x^2+14x+49)dx

    Thank you
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  2. #2
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    Quote Originally Posted by kinto View Post
    Hi,
    I would like some help evaluating the following integrals.
    I'm not sure if I am doing all the right steps.


    xcos^{2}(2x)dx

    ln(x^2+14x+49)dx

    Thank you

    Show us the steps you've done and where you think you may be wrong.
    The first one may be easily done by integration by parts knowing that INT(cos^2(t) dt) = [x + sin x cos x]/2.
    The second one requires from you to know INT(ln x)dx , which can be done straight integrating by parts, and also to put x^2 + 14x + 49 = (x+7)^2 and use some basic properties of logaritms.

    Tonio
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  3. #3
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    For the first one, I tried replacing my cos^2(2x) by using a half-angle identity

    x((1+cos4x)/2)dx
    1/2∫ x(1+cos4x)

    u=x
    du=dx

    dv=cos4x
    v= -1/4sin4x

    1/2[(x^2/2)+x((-1/4)sin4x)-(1/4)cos4x]
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  4. #4
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    Quote Originally Posted by kinto View Post
    Hi,
    I would like some help evaluating the following integrals.
    I'm not sure if I am doing all the right steps.


    xcos^{2}(2x)dx

    ln(x^2+14x+49)dx

    Thank you
    For the second one, try simplifying x^2+14x+49. You might see the rest of the steps after .
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