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Binomial Coefficients

Evaluate ∫2 x...

Question

Evaluate $\int \frac{2 x + 4}{x^{2} + 2 x} d x$
(where $C$ is constant of integration)

A

ln | x | + C

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B

2 ln | x | + C

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C

3 ln | x | + C

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D

ln | x + 2 | + C

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Solution

The correct option is B $2 ln | x | + C$
Let $I = \int \frac{(2 x + 4)}{(x^{2} + 2 x)} d x$
$\Rightarrow I = \int \frac{2 (x + 2)}{x (x + 2)} d x = \int \frac{2 d x}{x} = 2 ln | x | + C$

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