int frac{x - 1}{(x - 3)(x - 2)} , dx = | vedclass

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Question

(B) To solve the integral $\int \frac{x - 1}{(x - 3)(x - 2)} \, dx$,we use partial fractions. $\frac{x - 1}{(x - 3)(x - 2)} = \frac{A}{x - 3} + \frac{

Vedclass · Accepted Answer

$\log |(x - 3)^2| - \log |x - 2| + c$

Vedclass · Answer

(B) To solve the integral $\int \frac{x - 1}{(x - 3)(x - 2)} \, dx$,we use partial fractions. $\frac{x - 1}{(x - 3)(x - 2)} = \frac{A}{x - 3} + \frac{B}{x - 2}$.Multiplying by $(x - 3)(x - 2)$,we get $x - 1 = A(x - 2) + B(x - 3)$.For $x = 3$,$3 - 1 = A(3 - 2) \Rightarrow A = 2$.For $x = 2$,$2 - 1 = B(2 - 3) \Rightarrow B = -1$.Thus,$\int \left( \frac{2}{x - 3} - \frac{1}{x - 2} \right) \, dx = 2 \log |x - 3| - \log |x - 2| + c$.Using logarithmic properties,this is $\log |(x - 3)^2| - \log |x - 2| + c$.

$\int \frac{x - 1}{(x - 3)(x - 2)} \, dx = $

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