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$\int_{5}^{10}\left(3x+\ln\left(\frac{16x}{5}\right)\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function 3x+ln((2x*8)/5) from 5 to 10. Simplifying. Expand the integral \int_{5}^{10}\left(3x+\ln\left(\frac{16x}{5}\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\ln\left(\frac{16x}{5}\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du.