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# Integrate the function $\frac{1}{2x^2\left(x-1\right)}$ from $- \infty$ to $\infty$

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##  Final answer to the problem

The integral diverges.

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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

$\frac{1}{2}\int\frac{1}{x^2\left(x-1\right)}dx$

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. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by x^2\left(x-1\right). Multiplying polynomials.

##  Final answer to the problem

The integral diverges.

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

###  Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b