The correct option is C x 10ln|x+10|+C ∫xx+10dx =∫x+10 10x+10dx =∫x+10x+10dx 10∫dxx+10 =∫dx 10∫dxx+10 =x 10ln|x+10|+C ...

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Higher Order Derivatives

Integrate ∫...

Question

Integrate $\int \frac{x}{x + 10} d x$

x + 10 ln | x + 10 | + C

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x - 10 ln | x + 10 | + C

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x + 10 ln | x | + C

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Solution

The correct option is C $x - 10 ln | x + 10 | + C$
$\int \frac{x}{x + 10} d x$

$= \int \frac{x + 10 - 10}{x + 10} d x$

$= \int \frac{x + 10}{x + 10} d x - 10 \int \frac{d x}{x + 10}$

$= \int d x - 10 \int \frac{d x}{x + 10}$

$= x - 10 ln | x + 10 | + C$

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