Exercise
$\int\frac{x^5-x^4+2x^3-x}{x^3+1}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((x^5-x^42x^3-x)/(x^3+1))dx. Divide x^5-x^4+2x^3-x by x^3+1. Resulting polynomial. Expand the integral \int\left(x^{2}-x+2+\frac{-x^{2}-2}{x^3+1}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{2}dx results in: \frac{x^{3}}{3}.
Find the integral int((x^5-x^42x^3-x)/(x^3+1))dx
Final answer to the exercise
$\frac{x^{3}}{3}-\frac{1}{2}x^2+2x+\frac{-\arctan\left(\frac{x}{\sqrt{1-x}}\right)}{\sqrt{1-x}}-\ln\left|x+1\right|+C_0$