$\int \frac{c o s x + x s i n x}{x (x + c o s x)} d x =$

l o g | \frac{x}{x + c o s x} | + c

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- l o g | \frac{x}{x + c o s x} | + c

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l o g | \frac{x + c o s x}{2 x} | + c

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- l o g | \frac{x + c o s x}{2 x} | + c

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Solution

The correct option is A $l o g | \frac{x}{x + c o s x} | + c$
$\int \frac{x + c o s x + x s i n x - x}{x (x + c o s x)} d x = \int \frac{x + c o s x}{x (x + c o s x)} d x - \int \frac{x - x s i n x}{x (x + c o s x)} d x = l n x - l n | x + c o s x | = l o g | \frac{x}{x + c o s x} | + c$

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