Exercise
$\int x\arctan\left(x-1\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int(xarctan(x-1))dx. We can solve the integral \int x\arctan\left(x-1\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v. Solve the integral to find v.
Find the integral int(xarctan(x-1))dx
Final answer to the exercise
$\frac{1}{2}x^2\arctan\left(x-1\right)-\frac{1}{2}\ln\left|1+\left(x-1\right)^2\right|-\frac{1}{2}x+C_0$