Exercise
$\int\frac{x^6+x^3+x}{x+1}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((x^6+x^3x)/(x+1))dx. Divide x^6+x^3+x by x+1. Resulting polynomial. Expand the integral \int\left(x^{5}-x^{4}+x^{3}+1+\frac{-1}{x+1}\right)dx into 5 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{5}dx results in: \frac{x^{6}}{6}.
Find the integral int((x^6+x^3x)/(x+1))dx
Final answer to the exercise
$\frac{x^{6}}{6}+\frac{-x^{5}}{5}+\frac{x^{4}}{4}+x-\ln\left|x+1\right|+C_0$