Help me with this math problem?

How to integrate this integral? I've tried the partial fraction decomposition method but it doesn't seem to work at all. Please show all your work. Thanks.

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  • atsuo
    Lv 6
    1 year ago
    Favourite answer

    x^2+4x+4 = (x+2)^2 , so let x+2 = u and dx = du .

    ∫ 6x/(x^2+4x+4) dx

    = ∫ (6(x+2)-12)/((x+2)^2) dx

    = ∫ (6u-12)/(u^2) du

    = ∫ 6/u - 12/u^2 du

    = 6ln|u| + 12/u + C

    = 6ln|x+2| + 12/(x+2) + C

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