Exercise
$\int\frac{\left(x^3+2x^2+1\right)}{\left(x^2+1\right)}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((x^3+2x^2+1)/(x^2+1))dx. Divide x^3+2x^2+1 by x^2+1. Resulting polynomial. Expand the integral \int\left(x+2+\frac{-x-1}{x^2+1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int xdx results in: \frac{1}{2}x^2.
Find the integral int((x^3+2x^2+1)/(x^2+1))dx
Final answer to the exercise
$\frac{1}{2}x^2+2x-\arctan\left(x\right)-\frac{1}{2}\ln\left|x^2+1\right|+C_0$