Final Answer
Step-by-step Solution
Problem to solve:
Specify the solving method
Expand the fraction $\frac{\left(x^2+1\right)^2+5}{x^2+1}$ into $2$ simpler fractions with common denominator $x^2+1$
Learn how to solve integrals of rational functions problems step by step online.
$\int\left(\frac{\left(x^2+1\right)^2}{x^2+1}+\frac{5}{x^2+1}\right)dx$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int(((x^2+1)^2+5)/(x^2+1))dx. Expand the fraction \frac{\left(x^2+1\right)^2+5}{x^2+1} into 2 simpler fractions with common denominator x^2+1. Simplify the resulting fractions. Expand the integral \int\left(x^2+1+\frac{5}{x^2+1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^2dx results in: \frac{x^{3}}{3}.