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

Exercise

∫01 x3(x3+1)2dx\int_0^1\:\frac{x^3}{\left(x^3+1\right)^2}dx

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Final answer to the exercise

−118+−2327arctan⁡(13)+−327sin⁡(2θ)+2327arctan⁡(−13)+327sin⁡(2θ)+−32−9+32−9+19ln⁡∣2∣+−5327arctan⁡(−13)+5327arctan⁡(13)-\frac{1}{18}+\frac{-2\sqrt{3}}{27}\arctan\left(\frac{1}{\sqrt{3}}\right)+\frac{-\sqrt{3}}{27}\sin\left(2\theta \right)+\frac{2\sqrt{3}}{27}\arctan\left(\frac{-1}{\sqrt{3}}\right)+\frac{\sqrt{3}}{27}\sin\left(2\theta \right)+\frac{-\frac{3}{2}}{-9}+\frac{\frac{3}{2}}{-9}+\frac{1}{9}\ln\left|2\right|+\frac{-5\sqrt{3}}{27}\arctan\left(\frac{-1}{\sqrt{3}}\right)+\frac{5\sqrt{3}}{27}\arctan\left(\frac{1}{\sqrt{3}}\right)

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∫01 x3(x3+1)2 dx
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