Final answer to the problem
$x\arctan\left(x\right)-\frac{1}{2}\ln\left|1+x^2\right|+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Apply integration by parts: $u=arctan(x)$, $v'=1$
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$x\arctan\left(x\right)-\int\frac{x}{1+x^2}dx$
Learn how to solve problems step by step online. Solve the trigonometric integral int(arctan(x))dx. Apply integration by parts: u=arctan(x), v'=1. The integral -\int\frac{x}{1+x^2}dx results in: -\frac{1}{2}\ln\left(1+x^2\right). Gather the results of all integrals. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.
Final answer to the problem
$x\arctan\left(x\right)-\frac{1}{2}\ln\left|1+x^2\right|+C_0$
