Final answer to the problem
$\ln\left|x+1\right|+\frac{1}{x+1}+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Rewrite the expression $\frac{x}{x^2+2x+1}$ inside the integral in factored form
$\int\frac{x}{\left(x+1\right)^{2}}dx$
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$\int\frac{x}{\left(x+1\right)^{2}}dx$
Learn how to solve problems step by step online. Find the integral int(x/(x^2+2x+1))dx. Rewrite the expression \frac{x}{x^2+2x+1} inside the integral in factored form. Rewrite the fraction \frac{x}{\left(x+1\right)^{2}} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{x+1}+\frac{-1}{\left(x+1\right)^{2}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{x+1}dx results in: \ln\left|x+1\right|.
Final answer to the problem
$\ln\left|x+1\right|+\frac{1}{x+1}+C_0$
