Find the integral int(1/(x(x+1)(x^2+2)(x^2+3)^2))dx | SnapXam

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 Exercise

\int\frac{1}{x\left(x+1\right)\left(x^2+2\right)\left(x^2+3\right)^2}dx

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Final answer to the exercise  

\frac{1}{18}\ln\left|x\right|-\frac{1}{48}\ln\left|x+1\right|+\frac{-\arctan\left(\frac{x}{\sqrt{2}}\right)}{3\sqrt{2}}-\frac{1}{6}\ln\left|\sqrt{x^2+2}\right|+\frac{x}{24\left(x^2+3\right)}+\frac{\sqrt{3}\arctan\left(\frac{x}{\sqrt{3}}\right)}{72}+\frac{1}{-24\left(x^2+3\right)}+\frac{5\arctan\left(\frac{x}{\sqrt{3}}\right)}{16\sqrt{3}}-\frac{19}{144}\ln\left|\frac{\sqrt{3}}{\sqrt{x^2+3}}\right|+C_1

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Integrate by partial fractions
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Integrate using trigonometric identities
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Product of Binomials with Common Term
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∫1x(x+1)(x²+2)(x²+3)² dx

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