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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. The integral \int_{0}^{4}\frac{x}{x-4}dx results in: 4+\lim_{c\to0}\left(- \infty \right). Gather the results of all integrals. The integral \int_{4}^{6}\frac{x}{x-4}dx results in: 2+\lim_{c\to4}\left(2.772589-4\ln\left(c-4\right)\right).