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

Exercise

∫x4+1(x2−x+2)(x+1)dx\int\frac{x^4+1}{\left(x^2-x+2\right)\left(x+1\right)}dx

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Final answer to the exercise

12x2+−37arctan⁡(2(x−12)7)14−32ln⁡∣(x−12)2+74∣+12ln⁡∣x+1∣+C2\frac{1}{2}x^2+\frac{-3\sqrt{7}\arctan\left(\frac{2\left(x-\frac{1}{2}\right)}{\sqrt{7}}\right)}{14}-\frac{3}{2}\ln\left|\sqrt{\left(x-\frac{1}{2}\right)^2+\frac{7}{4}}\right|+\frac{1}{2}\ln\left|x+1\right|+C_2

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∫x4+1(x2−x+2)(x+1) dx
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