Learn how to solve simplify trigonometric expressions problems step by step online. Solve the integral of logarithmic functions int(ln((x^2-1)^(1/2)))dx. Apply properties of logarithms to expand and simplify the logarithmic expression \ln\left(\sqrt{x^2-1}\right) inside the integral. Expand the integral \int\left(\frac{1}{2}\ln\left(x+1\right)+\frac{1}{2}\ln\left(x-1\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{2}\ln\left(x+1\right)dx results in: \frac{1}{2}\left(\left(x+1\right)\ln\left(x+1\right)-x-1\right). The integral \int\frac{1}{2}\ln\left(x-1\right)dx results in: \frac{1}{2}\left(\left(x-1\right)\ln\left(x-1\right)-x+1\right).

Solve the integral of logarithmic functions int(ln((x^2-1)^(1/2)))dx