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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 $\frac{x^2+3x+2}{\left(x-1\right)^3\left(x+2\right)^2\left(x+1\right)}$ inside the integral in factored form
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$\int\frac{1}{\left(x-1\right)^3\left(x+2\right)}dx$
Learn how to solve problems step by step online. Find the integral int((x^2+3x+2)/((x-1)^3(x+2)^2(x+1)))dx. Rewrite the expression \frac{x^2+3x+2}{\left(x-1\right)^3\left(x+2\right)^2\left(x+1\right)} inside the integral in factored form. Rewrite the fraction \frac{1}{\left(x-1\right)^3\left(x+2\right)} in 4 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{3\left(x-1\right)^3}+\frac{-1}{27\left(x+2\right)}+\frac{1}{27\left(x-1\right)}+\frac{-1}{9\left(x-1\right)^{2}}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{3\left(x-1\right)^3}dx results in: \frac{-1}{6\left(x-1\right)^{2}}.
