Exercise
$\int\frac{6x+2}{7x^2+2x}dx$
Step-by-step Solution
Learn how to solve integral calculus problems step by step online. Find the integral int((6x+2)/(7x^2+2x))dx. Rewrite the expression \frac{6x+2}{7x^2+2x} inside the integral in factored form. Rewrite the fraction \frac{6x+2}{x\left(7x+2\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{x}+\frac{-1}{7x+2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{x}dx results in: \ln\left(x\right).
Find the integral int((6x+2)/(7x^2+2x))dx
Final answer to the exercise
$\ln\left|x\right|-\frac{1}{7}\ln\left|7x+2\right|+C_0$