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Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$
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$\int\left(\ln\left(\sqrt[5]{x}\right)+\ln\left(\left(x^2-4\right)^7e^x\right)\right)dx$
Learn how to solve problems step by step online. Solve the integral of logarithmic functions int(ln(x^1/5(x^2-4)^7e^x))dx. 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(\sqrt[5]{x}\right)+\ln\left(\left(x^2-4\right)^7e^x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\ln\left(\sqrt[5]{x}\right)dx results in: \frac{1}{5}x\ln\left(x\right)+\frac{-x}{5}. Gather the results of all integrals.