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
Learn how to solve integration by trigonometric substitution 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
$x\arctan\left(x\right)-\frac{1}{2}\ln\left|1+x^2\right|+C_0$
