∫dxsin xcos x #160; = 2∫dx2sin x cosx = 2∫dxsin 2x #160; = 2∫cos ec2xdx = 2ln| cosec 2x cot2x2|dx ...

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Substitution Method to Remove Indeterminate Form

∫dxsin xcos x

Question

$\int \frac{d x}{sin x cos x}$

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Solution

$\int \frac{d x}{sin x cos x} = 2 \int \frac{d x}{2 sin x cosx} = 2 \int \frac{d x}{sin 2 x} = 2 \int cos e c 2 x d x = 2 ln ∣ ∣ ∣ \frac{cosec 2 x - c o t 2 x}{2} ∣ ∣ ∣ d x$

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