Final answer to the problem
$\ln\left|2x+1\right|+2x+C_1$
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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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- Product of Binomials with Common Term
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1
Take out the constant $4$ from the integral
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$4\int\frac{x+1}{2x+1}dx$
Learn how to solve problems step by step online. Find the integral int((4(x+1))/(2x+1))dx. Take out the constant 4 from the integral. Expand the fraction \frac{x+1}{2x+1} into 2 simpler fractions with common denominator 2x+1. Expand the integral \int\left(\frac{x}{2x+1}+\frac{1}{2x+1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral 4\int\frac{x}{2x+1}dx results in: 2x+1-\ln\left(2x+1\right).
Final answer to the problem
$\ln\left|2x+1\right|+2x+C_1$
