Evaluate the indefinite integral ∫x3+2x2+3x+4(x2+1)2 dx\int \frac{x^3 + 2x^2 + 3x + 4}{(x^2 + 1)^2} \, dx∫(x2+1)2x3+2x2+3x+4dx.
x/(x2+1)+arctan(x)+Cx/(x^2 + 1) + \arctan(x) + Cx/(x2+1)+arctan(x)+C
x/(x2+1)−ln∣x2+1∣+Cx/(x^2 + 1) - \ln|x^2 + 1| + Cx/(x2+1)−ln∣x2+1∣+C
−x/(x2+1)+ln∣x2+1∣+C-x/(x^2 + 1) + \ln|x^2 + 1| + C−x/(x2+1)+ln∣x2+1∣+C
12ln(x2+1)+3arctan(x)+xx2+1−1x2+1+C\frac{1}{2}\ln(x^2 + 1) + 3\arctan(x) + \frac{x}{x^2 + 1} - \frac{1}{x^2 + 1} + C21ln(x2+1)+3arctan(x)+x2+1x−x2+11+C
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