Integrate the function $\frac{x+2}{2x^2-4x}$ from $-2$ to $1$

Step-by-step Solution

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Final answer to the problem

The integral diverges.

Step-by-step Solution

How should I solve this problem?

  • Integrate by trigonometric substitution
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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Since the integral $\int_{-2}^{1}\frac{x+2}{2x^2-4x}dx$ has a discontinuity inside the interval, we have to split it in two integrals

$\int_{-2}^{0}\frac{x+2}{2x^2-4x}dx+\int_{0}^{1}\frac{x+2}{2x^2-4x}dx$

Learn how to solve differential equations problems step by step online.

$\int_{-2}^{0}\frac{x+2}{2x^2-4x}dx+\int_{0}^{1}\frac{x+2}{2x^2-4x}dx$

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Learn how to solve differential equations problems step by step online. Integrate the function (x+2)/(2x^2-4x) from -2 to 1. Since the integral \int_{-2}^{1}\frac{x+2}{2x^2-4x}dx has a discontinuity inside the interval, we have to split it in two integrals. The integral \int_{-2}^{0}\frac{x+2}{2x^2-4x}dx results in: \int_{-2}^{0}\frac{x}{2x^2-4x}dx+\int_{-2}^{0}\frac{1}{x^2-2x}dx. Gather the results of all integrals. The integral \int_{0}^{1}\frac{x+2}{2x^2-4x}dx results in: \int_{0}^{1}\frac{x}{2x^2-4x}dx+\int_{0}^{1}\frac{1}{x^2-2x}dx.

Final answer to the problem

The integral diverges.

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Function Plot

Plotting: $\frac{x+2}{2x^2-4x}$

Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

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