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$\int_{0}^{1}\frac{x+2}{5x+1}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (x+2)/(x^2^1/2+4x+1) from 0 to 1. Simplify the expression inside the integral. Expand the fraction \frac{x+2}{5x+1} into 2 simpler fractions with common denominator 5x+1. Expand the integral \int_{0}^{1}\left(\frac{x}{5x+1}+\frac{2}{5x+1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int_{0}^{1}\frac{x}{5x+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 5x+1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.