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f(x)=(5x^4+x^26x+1)/(x^2(x^2+x+1)^2)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫(5x4+x2+6x+1x2(x2+x+1)2)dx\int\left(\frac{5x^4+x^2+6x+1}{x^2\left(x^2+x+1\right)^2}\right)dx

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Final answer to the exercise

1−x−10ln⁡∣x+1∣+14ln⁡∣x∣+10x+43arctan⁡(2(x+12)3)3−4ln⁡∣(x+12)2+34∣+C2\frac{1}{-x}-10\ln\left|x+1\right|+14\ln\left|x\right|+\frac{10}{x}+\frac{4\sqrt{3}\arctan\left(\frac{2\left(x+\frac{1}{2}\right)}{\sqrt{3}}\right)}{3}-4\ln\left|\sqrt{\left(x+\frac{1}{2}\right)^2+\frac{3}{4}}\right|+C_2

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∫(5x4+x2+6x+1x2(x2+x+1)2 )dx
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