Final answer to the problem
Step-by-step Solution
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Multiplying the fraction by $x-2$
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$\int\frac{x-2}{x+1}dx$
Learn how to solve integral calculus problems step by step online. Find the integral int(1/(x+1)(x-2))dx. Multiplying the fraction by x-2. Expand the fraction \frac{x-2}{x+1} into 2 simpler fractions with common denominator x+1. Expand the integral \int\left(\frac{x}{x+1}+\frac{-2}{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.