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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Originally Posted by cupcakelova87 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
Originally Posted by cupcakelova87 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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