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Math Help - An Intergral Check

  1. #1
    Junior Member Selim's Avatar
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    An Intergral Check

    \int x^n sin(x) * dx = ______________________ + \int x^{n-1} cos(x) * dx

    I want to just say sin(x), but that n should be a +1 and not minus or am I wrong? And,

    Evaluate \int 5x * sin(x) * dx

    Would you just pull the 5 out and call it a day or what?
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  2. #2
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    Quote Originally Posted by Selim View Post
    \int x^n sin(x) * dx = ______________________ + \int x^{n-1} cos(x) * dx

    I want to just say sin(x), but that n should be a +1 and not minus or am I wrong? And,

    Evaluate \int 5x * sin(x) * dx

    Would you just pull the 5 out and call it a day or what?
    in the blank cos(x) will come as it is the integration of sin(x). in ur second question as u said simply pull out 5 and integrate by parts.
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  3. #3
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    Quote Originally Posted by Selim View Post
    \int x^n sin(x) * dx = ______________________ + \int x^{n-1} cos(x) * dx

    I want to just say sin(x), but that n should be a +1 and not minus or am I wrong? And,

    Evaluate \int 5x * sin(x) * dx

    Would you just pull the 5 out and call it a day or what?
    Using integration by parts

    Let u = x^n so that du = nx^{n - 1}

    Let dv = \sin{x} so that v = -\cos{x}.


    Then \int{x^n\sin{x}\,dx} = -x^n\cos{x} - \int{-nx^{n - 1}\cos{x}\,dx}

     = -x^n\cos{x} + n\int{x^{n - 1}\cos{x}\,dx}.
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  4. #4
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    never mind
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