Calc 1

Evaluate the integral by making the given substitution. (Use C for the constant of integration.)

∫ dt/(1-7)^7, u=1-7t

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  1. I suspect you mean

    ∫ dt/(1-7t)^7, u=1-7t

    so if u = 1-7t
    then du = -7 dt
    or dt = -du/7

    so we have
    ∫( -du/7)/u^7
    or
    -(1/7) ∫ u^-7 du

    -(1/7)(-1/6) u^-6

    (1/42) u^-6 + C
    1/[42(1-7t)^6] + C

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