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Expand the fraction $\frac{x+3}{x^2+2x}$ into $2$ simpler fractions with common denominator $x^2+2x$
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$\int\left(\frac{x}{x^2+2x}+\frac{3}{x^2+2x}\right)dx$
Learn how to solve problems step by step online. Find the integral int((x+3)/(x^2+2x))dx. Expand the fraction \frac{x+3}{x^2+2x} into 2 simpler fractions with common denominator x^2+2x. Expand the integral \int\left(\frac{x}{x^2+2x}+\frac{3}{x^2+2x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Rewrite the expression \frac{x}{x^2+2x} inside the integral in factored form. We can solve the integral \int\frac{1}{x+2}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+2 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.