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Since the integral $\int_{0}^{6}\frac{x}{x-4}dx$ has a discontinuity inside the interval, we have to split it in two integrals
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$\int_{0}^{4}\frac{x}{x-4}dx+\int_{4}^{6}\frac{x}{x-4}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function x/(x-4) from 0 to 6. Since the integral \int_{0}^{6}\frac{x}{x-4}dx has a discontinuity inside the interval, we have to split it in two integrals. Rewrite the fraction \frac{x}{x-4} inside the integral as the product of two functions: x\frac{1}{x-4}. We can solve the integral \int x\frac{1}{x-4}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.