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