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$\int\ln\left(\sqrt{\frac{\left(x-8\right)^{26}}{\left(3x-7\right)^{38}}}\right)dx$
Learn how to solve integrals of exponential functions problems step by step online. Find the integral of ln((((x-8)^26)/((3x-7)^38))^1/2). Find the integral. Apply properties of logarithms to expand and simplify the logarithmic expression \ln\left(\sqrt{\frac{\left(x-8\right)^{26}}{\left(3x-7\right)^{38}}}\right) inside the integral. Expand the integral \int\left(13\ln\left(x-8\right)-19\ln\left(3x-7\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int13\ln\left(x-8\right)dx results in: 13\left(\left(x-8\right)\ln\left(x-8\right)-x+8\right).