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f(x)=((x-1)^2(x+1))/((x^2+1)^3)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫(x−1)2(x+1)(x2+1)3dx\int\frac{\left(x-1\right)^2\left(x+1\right)}{\left(x^2+1\right)^3}dx

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Final answer to the exercise

x44(x2+1)2+34arctan⁡(x)+12x(x2+1)2+xx2+1−12arctan⁡(x)+14(x2+1)2+3x8(x2+1)+C0\frac{x^{4}}{4\left(x^2+1\right)^{2}}+\frac{3}{4}\arctan\left(x\right)+\frac{\frac{1}{2}x}{\left(x^2+1\right)^{2}}+\frac{x}{x^2+1}-\frac{1}{2}\arctan\left(x\right)+\frac{1}{4\left(x^2+1\right)^{2}}+\frac{3x}{8\left(x^2+1\right)}+C_0

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∫(x−1)2(x+1)(x2+1)3 dx
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