Evaluate ∫x2(x+1)3 dx\int \frac{x^2}{(x+1)^3}\,dx∫(x+1)3x2dx (simplify by polynomial long division or substitution u=x+1u=x+1u=x+1).
ln∣x+1∣−2x+1+12(x+1)2+C\ln|x+1| - \frac{2}{x+1} + \frac{1}{2(x+1)^2} + Cln∣x+1∣−x+12+2(x+1)21+C
−x22(x+1)2+C-\frac{x^2}{2(x+1)^2} + C−2(x+1)2x2+C
ln∣x+1∣+2x+1+C\ln|x+1| + \frac{2}{x+1} + Cln∣x+1∣+x+12+C
1x+1+C\frac{1}{x+1} + Cx+11+C