Final answer to the problem
The integral diverges.
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 $\frac{3}{3x-x^2}$ inside the integral in factored form
Learn how to solve improper integrals problems step by step online.
$\int\frac{3}{x\left(3-x\right)}dx$
Learn how to solve improper integrals problems step by step online. Integrate the function 3/(3x-x^2) from -infinity to -1. Rewrite the expression \frac{3}{3x-x^2} inside the integral in factored form. Rewrite the fraction \frac{3}{x\left(3-x\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{x}+\frac{1}{3-x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{x}dx results in: \ln\left(x\right).
Final answer to the problem
The integral diverges.
