Final answer to the problem
Step-by-step Solution
Specify the solving method
Find the integral
Learn how to solve integral calculus problems step by step online.
$\int\ln\left(\sqrt[7]{\frac{x^2+1}{x^2-1}}\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral of ln(((x^2+1)/(x^2-1))^1/7). Find the integral. Apply properties of logarithms to expand and simplify the logarithmic expression \ln\left(\sqrt[7]{\frac{x^2+1}{x^2-1}}\right) inside the integral. Expand the integral \int\left(\frac{1}{7}\ln\left(x^2+1\right)-\frac{1}{7}\ln\left(x+1\right)-\frac{1}{7}\ln\left(x-1\right)\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{7}\ln\left(x^2+1\right)dx results in: \frac{1}{7}\left(\left(x^2+1\right)\ln\left(x^2+1\right)-x^2-1\right).