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Choose the correct answer
Choose the correct answer in each of the following :
$\int \frac{x d x}{(x-1)(x-2)}$ equals
(a) $\log \left|\frac{(x-1)^2}{x-2}\right|+C$
(b) $\log \left|\frac{(x-2)^2}{x-1}\right|+C$
(c) $\log \left|\left(\frac{x-1^2}{x-2}\right)\right|+C$ (d) $\log |(x-1)(x-2)|+C$
Choose the correct answer in each of the following :
$\int \frac{x d x}{(x-1)(x-2)}$ equals
(a) $\log \left|\frac{(x-1)^2}{x-2}\right|+C$
(b) $\log \left|\frac{(x-2)^2}{x-1}\right|+C$
(c) $\log \left|\left(\frac{x-1^2}{x-2}\right)\right|+C$ (d) $\log |(x-1)(x-2)|+C$
Solution:
1836 Upvotes
Verified Answer
(b)
$\begin{aligned}
&\int \frac{x}{(x-1)(x-2)} d x=\int\left[\frac{-1}{x-1}+\frac{2}{x-2}\right] d x \\
&=\log \left[\frac{(x-2)^2}{x-1}\right]+\mathrm{C}
\end{aligned}$
$\begin{aligned}
&\int \frac{x}{(x-1)(x-2)} d x=\int\left[\frac{-1}{x-1}+\frac{2}{x-2}\right] d x \\
&=\log \left[\frac{(x-2)^2}{x-1}\right]+\mathrm{C}
\end{aligned}$
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