Exercise
$4\int\left(\frac{e^x-1}{3x}\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral 4int((e^x-1)/(3x))dx. Take the constant \frac{1}{3} out of the integral. Multiply the fraction and term in 4\cdot \left(\frac{1}{3}\right)\int\frac{e^x-1}{x}dx. Expand the fraction \frac{e^x-1}{x} into 2 simpler fractions with common denominator x. Expand the integral \int\left(\frac{e^x}{x}+\frac{-1}{x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Find the integral 4int((e^x-1)/(3x))dx
Final answer to the exercise
$\frac{4}{3}Ei\left(x\right)-\frac{4}{3}\ln\left|x\right|+C_0$