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

Exercise

∫x3+2x(x2+2x+2)(x2+5)dx\int\frac{x^3+2x}{\left(x^2+2x+2\right)\left(x^2+5\right)}dx

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Final answer to the exercise

−829arctan⁡(x+1)+1029ln⁡∣(x+1)2+1∣+−30arctan⁡(x5)295+929ln⁡∣x2+5∣+C1-\frac{8}{29}\arctan\left(x+1\right)+\frac{10}{29}\ln\left|\left(x+1\right)^2+1\right|+\frac{-30\arctan\left(\frac{x}{\sqrt{5}}\right)}{29\sqrt{5}}+\frac{9}{29}\ln\left|\sqrt{x^2+5}\right|+C_1

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∫x3+2x(x2+2x+2)(x2+5) dx
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