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

Exercise

∫(x2+2x+3)(x3(x−1)((x+3))2)dx\int\frac{\left(x^2+2x+3\right)}{\left(x^3\left(x-1\right)\left(\left(x+3\right)\right)^2\right)}dx

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Final answer to the exercise

16x2+38ln⁡∣x−1∣+−118(x+3)−1127ln⁡∣x∣+13x+7216ln⁡∣x+3∣+C0\frac{1}{6x^{2}}+\frac{3}{8}\ln\left|x-1\right|+\frac{-1}{18\left(x+3\right)}-\frac{11}{27}\ln\left|x\right|+\frac{1}{3x}+\frac{7}{216}\ln\left|x+3\right|+C_0

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∫(x2+2x+3)(x3(x−1)((x+3))2) dx
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