Final answer to the problem
$2\ln\left|x-3\right|-\ln\left|x-2\right|+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
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- Weierstrass Substitution
- Integrate using trigonometric identities
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- Product of Binomials with Common Term
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1
Rewrite the fraction $\frac{x-1}{\left(x-3\right)\left(x-2\right)}$ in $2$ simpler fractions using partial fraction decomposition
$\frac{2}{x-3}+\frac{-1}{x-2}$
Learn how to solve problems step by step online. Find the integral int((x-1)/((x-3)(x-2)))dx. Rewrite the fraction \frac{x-1}{\left(x-3\right)\left(x-2\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{2}{x-3}+\frac{-1}{x-2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{2}{x-3}dx results in: 2\ln\left(x-3\right). The integral \int\frac{-1}{x-2}dx results in: -\ln\left(x-2\right).
Final answer to the problem
$2\ln\left|x-3\right|-\ln\left|x-2\right|+C_0$
