int frac{dx}{tan x + cot x + sec x + csc x} = | vedclass

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(B) Let $I = \int \frac{dx}{	an x + \cot x + \sec x + \csc x}$.$= \int \frac{dx}{\left(\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} + \frac{1}{\cos

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$\frac{1}{2} (\sin x - \cos x - x) + c$

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(B) Let $I = \int \frac{dx}{	an x + \cot x + \sec x + \csc x}$.$= \int \frac{dx}{\left(\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} + \frac{1}{\cos x} + \frac{1}{\sin x}ight)}$$= \int \frac{\sin x \cos x}{\sin^{2} x + \cos^{2} x + \sin x + \cos x} dx$$= \int \frac{\sin x \cos x}{1 + \sin x + \cos x} dx$Multiply numerator and denominator by $(\sin x + \cos x - 1)$:$= \int \frac{\sin x \cos x (\sin x + \cos x - 1)}{(\sin x + \cos x)^{2} - 1} dx$$= \int \frac{\sin x \cos x (\sin x + \cos x - 1)}{\sin^{2} x + \cos^{2} x + 2 \sin x \cos x - 1} dx$$= \int \frac{\sin x \cos x (\sin x + \cos x - 1)}{2 \sin x \cos x} dx$$= \frac{1}{2} \int (\sin x + \cos x - 1) dx$$= \frac{1}{2} (-\cos x + \sin x - x) + c$.

$\int \frac{dx}{\tan x + \cot x + \sec x + \csc x} =$

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