Final answer to the problem
$\ln\left|x\right|+\frac{1}{2\left(x^2+1\right)}-\frac{1}{2}\ln\left|x^2+1\right|+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
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- Weierstrass Substitution
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1
Rewrite the fraction $\frac{1}{x\left(x^2+1\right)^2}$ in $3$ simpler fractions using partial fraction decomposition
$\frac{1}{x}+\frac{-x}{\left(x^2+1\right)^2}+\frac{-x}{x^2+1}$
Learn how to solve integrals by partial fraction expansion problems step by step online.
$\frac{1}{x}+\frac{-x}{\left(x^2+1\right)^2}+\frac{-x}{x^2+1}$
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(1/(x(x^2+1)^2))dx. Rewrite the fraction \frac{1}{x\left(x^2+1\right)^2} in 3 simpler fractions using partial fraction decomposition. Simplify the expression. The integral \int\frac{1}{x}dx results in: \ln\left(x\right). The integral -\int\frac{x}{\left(x^2+1\right)^2}dx results in: \frac{1}{2\left(x^2+1\right)}.
Final answer to the problem
$\ln\left|x\right|+\frac{1}{2\left(x^2+1\right)}-\frac{1}{2}\ln\left|x^2+1\right|+C_0$
