I = ∫dx/√(3)cos x+sin x = 1/2∫dx/√(3)/2cos x+sin x.1/2 #160; = 1/2∫dx/cos(x π/6) = 1/2∫ sec(x π/6)dx =1/2 [ln(sec(x π/6)+tan(x π/6)]+ ...

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Chain Rule of Differentiation

∫dx√3 cosx + ...

Question

$\int \frac{d x}{\sqrt{3} c o s x + s i n x}$

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Solution

$I = \int \frac{d x}{\sqrt{3} c o s x + s i n x}$
$= \frac{1}{2} \int \frac{d x}{\frac{\sqrt{3}}{2} c o s x + s i n x . \frac{1}{2}}$
$= \frac{1}{2} \int \frac{d x}{c o s (x - \frac{π}{6})}$
$= \frac{1}{2} \int s e c (x - \frac{π}{6}) d x$
$= \frac{1}{2} [l n (s e c (x - \frac{π}{6}) + t a n (x - \frac{π}{6})] + c$

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