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Exercise

$\int_{1}^{2}\frac{1}{x\cdot\left(x+1\right)}dx$

Step-by-step Solution

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Final answer to the exercise

$2\ln\left|2\right|-\ln\left|3\right|$

Exact Numeric Answer

$0.287682$

Try other ways to solve this exercise

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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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Similar Questions Solved

$\int_2^{\infty}\left(\frac{1}{x^2+x-2}\right)dx$

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

$\int\frac{1}{\left(x^4+1\right)}dx$

$\int\frac{dx}{x^2+7x-6}$

$\int\frac{dx}{x^2+7x+6}$

$\int_2^{\infty}\left(\frac{1}{x^2+6x+5}\right)dx$

$\int_0^{\infty}\left(\frac{1}{\sqrt{x}+x^2}\right)dx$

Main Topic: Integrals by Partial Fraction Expansion

The partial fraction decomposition or partial fraction expansion of a rational function is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

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