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Exercise

$\int\frac{4x^3-x+1}{x^3+1}dx$

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Final answer to the exercise

$4x-\frac{2}{3}\ln\left|x+1\right|+\frac{-4\arctan\left(\frac{-1+2x}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{2}{3}\ln\left|\sqrt{\left(x-\frac{1}{2}\right)^2+\frac{3}{4}}\right|+C_2$

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  • Integrate by partial fractions
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  • Integrate using tabular integration
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  • Product of Binomials with Common Term
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