# What is #int (x)/(x+1)^3 dx#?

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To solve the integral ∫(x)/(x+1)^3 dx, you would use partial fraction decomposition followed by integration by substitution:

∫(x)/(x+1)^3 dx = ∫[A/(x+1) + B/(x+1)^2 + C/(x+1)^3] dx = Aln|x+1| - B/(x+1) - C/(2(x+1)^2) + C'

where A = -1/2, B = 1, and C = 1/2. Therefore,

∫(x)/(x+1)^3 dx = -(1/2)ln|x+1| - 1/(x+1) - 1/(2(x+1)^2) + C.

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