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Expand the fraction $\frac{x+5}{x^2-1}$ into $2$ simpler fractions with common denominator $x^2-1$
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$\int\left(\frac{x}{x^2-1}+\frac{5}{x^2-1}\right)dx$
Learn how to solve problems step by step online. Find the integral int((x+5)/(x^2-1))dx. Expand the fraction \frac{x+5}{x^2-1} into 2 simpler fractions with common denominator x^2-1. Expand the integral \int\left(\frac{x}{x^2-1}+\frac{5}{x^2-1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Rewrite the fraction \frac{x}{x^2-1} inside the integral as the product of two functions: x\frac{1}{x^2-1}. We can solve the integral \int x\frac{1}{x^2-1}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula.