The correct option is A log| x x+1 | +c ∫ dx x( x+1 ) nbsp; nbsp; =∫ 1 x dx ∫ 1 x+1 dx nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Property 2

Solve ∫ dx ...

Question

Solve $\int \frac{d x}{x (x + 1)}$

log ∣ ∣ ∣ \frac{x + 1}{x} ∣ ∣ ∣ + c

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log ∣ ∣ ∣ \frac{x}{x + 1} ∣ ∣ ∣ + c

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log ∣ ∣ ∣ \frac{x - 1}{x} ∣ ∣ ∣ + c

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log ∣ ∣ ∣ \frac{x - 1}{x + 1} ∣ ∣ ∣ + c

where

c

is an arbitrary constant

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Solution

The correct option is A $log ∣ ∣ ∣ \frac{x}{x + 1} ∣ ∣ ∣ + c$
$\int \frac{d x}{x (x + 1)} = \int \frac{1}{x} d x - \int \frac{1}{x + 1} d x$
$= log x - log (x + 1) + c$
$= log ∣ ∣ ∣ \frac{x}{x + 1} ∣ ∣ ∣ + c$

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