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Math Help - Integral Problem

  1. #1
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    Integral Problem

    Use formal substitution to find the integral of:
    (1 + 1/t)^3 * (1 / t^2)dt

    Any help is much appreciated!
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  2. #2
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    Quote Originally Posted by cupcakelova87 View Post
    Use formal substitution to find the integral of:
    (1 + 1/t)^3 * (1 / t^2)dt

    Any help is much appreciated!
    int[(1 + (1/t))^3 + (1/(t^2))dt]

    Expand:

    int[(t^3 + 3t^2 + 4t + 1)/t^3]

    Expand further:

    int[(3/t) + (4/t^2) + (1/t^3) + 1]

    Thus,

    int[(3/t) + (4/t^2) + (1/t^3) + 1] = 3*ln(t) + (-4/t) + (-1/(2*t^2)) + t + C

    = 3*ln(t) - 4/t - 1/(2t^2) + t + C
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  3. #3
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    Quote Originally Posted by cupcakelova87 View Post
    Use formal substitution to find the integral of:
    (1 + 1/t)^3 * (1 / t^2)dt

    Any help is much appreciated!
    Let x = 1 + 1/t. Then dx = -1/t^2 dt

    So:
    Int[(1 + 1/t^2)^3 * (1/t^2) dt]

    = Int[-(1 + 1/t^2)^3 * (-1/t^2) dt]

    = Int[-x^3 * dx]

    = -(1/4)x^4 + C

    = -(1/4)*(1 + 1/t)^4 + C

    -Dan
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