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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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Rewrite the expression $\frac{1}{x^2+6x+5}$ inside the integral in factored form

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$\int\frac{1}{\left(x+1\right)\left(x+5\right)}dx$

Learn how to solve problems step by step online. Integrate the function 1/(x^2+6x+5) from 2 to infinity. Rewrite the expression \frac{1}{x^2+6x+5} inside the integral in factored form. Rewrite the fraction \frac{1}{\left(x+1\right)\left(x+5\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{4\left(x+1\right)}+\frac{-1}{4\left(x+5\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{4\left(x+1\right)}dx results in: \frac{1}{4}\ln\left(x+1\right).

** Final answer to the problem ** **

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