Exercise
$\int\left(\frac{\left(x^3+\ln\left(x\right)\right)}{x}\right)dx$
Step-by-step Solution
Learn how to solve integration by substitution problems step by step online. Solve the integral of logarithmic functions int((x^3+ln(x))/x)dx. Expand the fraction \frac{x^3+\ln\left(x\right)}{x} into 2 simpler fractions with common denominator x. Simplify the resulting fractions. Expand the integral \int\left(x^{2}+\frac{\ln\left(x\right)}{x}\right)dx into 2 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}.
Solve the integral of logarithmic functions int((x^3+ln(x))/x)dx
Final answer to the exercise
$\frac{x^{3}}{3}+\frac{1}{2}\ln\left|x\right|^2+C_0$