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$\int\ln\left(x\sqrt{x^2-1}\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral of ln(x(x^2-1)^1/2). Find the integral. Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Expand the integral \int\left(\ln\left(x\right)+\ln\left(\sqrt{x^2-1}\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\ln\left(x\right)dx results in: x\ln\left(x\right)-x.