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Math Help - Integration by parts help

  1. #1
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    Integration by parts help

    Use integration by parts


    Ans:
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  2. #2
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    Hello, ^_^Engineer_Adam^_^!

    This is a sneaky one . . .



    . . . . xe^x
    . . ∫ ---------
    . . . (1 + x)

    Let: . . .u .= .xe^x . . . . . . . dv .= .(1 + x)^{-2} dx

    Then: .du .= .e^x(1 + x) dx . . v .= .-(1 + x)^{-1}


    . . . . . . . . -xe^x . . . . .-1
    We have: . -------- .- .∫ ------- e^x(1 + x) dx
    . . . . . . . . .1 + x . . . . 1 + x

    . . . . . . . . .-xe^x
    . . . . . . = . -------- .+ .∫ e^x dx
    . . . . . . . . . 1 + x

    . . . . . . . . .-xe^x
    . . . . . . = . -------- + e^x + C
    . . . . . . . . . 1 + x

    . . . . . . . . . . . . . . .e^x
    This simplifies to: . ------- + C
    . . . . . . . . . . . . . . 1 + x

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