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$\int\frac{x+1}{x-1}dx$
Learn how to solve problems step by step online. Integrate the function (x+1)/(x-1). Find the integral. Expand the fraction \frac{x+1}{x-1} into 2 simpler fractions with common denominator x-1. Expand the integral \int\left(\frac{x}{x-1}+\frac{1}{x-1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{x}{x-1}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x-1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.