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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 fraction $\frac{1}{u\left(1+u\right)}$ in $2$ simpler fractions using partial fraction decomposition

Learn how to solve integrals of rational functions problems step by step online.

$\frac{1}{u}+\frac{-1}{1+u}$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int(1/(u(1+u)))du. Rewrite the fraction \frac{1}{u\left(1+u\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{u}+\frac{-1}{1+u}\right)du into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{u}du results in: \ln\left(u\right). The integral \int\frac{-1}{1+u}du results in: -\ln\left(u+1\right).

** Final answer to the problem ** **

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