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Since the integral $\int_{-1}^{1}\frac{1}{x}dx$ has a discontinuity inside the interval, we have to split it in two integrals
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$\int_{-1}^{0}\frac{1}{x}dx+\int_{0}^{1}\frac{1}{x}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function 1/x from -1 to 1. Since the integral \int_{-1}^{1}\frac{1}{x}dx has a discontinuity inside the interval, we have to split it in two integrals. The integral \int_{-1}^{0}\frac{1}{x}dx results in: \int_{-1}^{0}\frac{1}{x}dx+\int_{0}^{0}\frac{1}{x}dx. The integral \int_{-1}^{0}\frac{1}{x}dx results in: \int_{-1}^{0}\frac{1}{x}dx+\int_{0}^{0}\frac{1}{x}dx. Gather the results of all integrals.