Final answer to the problem
$\ln\left|2x+1\right|+x+C_1$
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Step-by-step Solution
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- Integrate by partial fractions
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- Weierstrass Substitution
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1
Expand the fraction $\frac{2x+3}{2x+1}$ into $2$ simpler fractions with common denominator $2x+1$
$\int\left(\frac{2x}{2x+1}+\frac{3}{2x+1}\right)dx$
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$\int\left(\frac{2x}{2x+1}+\frac{3}{2x+1}\right)dx$
Learn how to solve problems step by step online. Find the integral int((2x+3)/(2x+1))dx. Expand the fraction \frac{2x+3}{2x+1} into 2 simpler fractions with common denominator 2x+1. Simplify the expression. The integral 2\int\frac{x}{2x+1}dx results in: x+\frac{1}{2}-\frac{1}{2}\ln\left(2x+1\right). Gather the results of all integrals.
Final answer to the problem
$\ln\left|2x+1\right|+x+C_1$
