Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- 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
- FOIL Method
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When multiplying exponents with same base you can add the exponents: $\left(x+1\right)^2\left(x+1\right)\left(x-2\right)$
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$\int\frac{x^2+2}{\left(x+1\right)^{3}\left(x-2\right)}dx$
Learn how to solve problems step by step online. Find the integral int((x^2+2)/((x+1)^2(x+1)(x-2)))dx. When multiplying exponents with same base you can add the exponents: \left(x+1\right)^2\left(x+1\right)\left(x-2\right). Rewrite the fraction \frac{x^2+2}{\left(x+1\right)^{3}\left(x-2\right)} in 4 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-1}{\left(x+1\right)^{3}}+\frac{2}{9\left(x-2\right)}+\frac{-2}{9\left(x+1\right)}+\frac{1}{3\left(x+1\right)^{2}}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{-1}{\left(x+1\right)^{3}}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x+1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.