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1.	Integrate. dx/(sin2xcos2x)
Answer» \(\int\frac{d\mathrm x}{\sin^2\mathrm x\cos^2\mathrm x}\) \(=\int \frac{\sin^2\mathrm x+\cos^2\mathrm x}{\sin^2\mathrm x\cos^2\mathrm x}d\mathrm x\) (\(\because\) sin²x + cos²x = 1) \(=\int \frac{1}{\cos^2\mathrm x}d\mathrm x\) + \(\int \frac{1}{\sin^2\mathrm x}d\mathrm x\) \(=\int \sec^2\mathrm xd\mathrm x\) + \(\int \mathrm{cosec^2xd x}\) = tan x – cot x + C, where C is an integral constant. \((\because\) \(\int\)sec²x dx = tan x and \(\int\)cosec²x dx = –cot x)

Integrate. dx/(sin2xcos2x)

Answer»

\(\int\frac{d\mathrm x}{\sin^2\mathrm x\cos^2\mathrm x}\) \(=\int \frac{\sin^2\mathrm x+\cos^2\mathrm x}{\sin^2\mathrm x\cos^2\mathrm x}d\mathrm x\) (\(\because\) sin²x + cos²x = 1)

\(=\int \frac{1}{\cos^2\mathrm x}d\mathrm x\) + \(\int \frac{1}{\sin^2\mathrm x}d\mathrm x\)

\(=\int \sec^2\mathrm xd\mathrm x\) + \(\int \mathrm{cosec^2xd x}\)

= tan x – cot x + C, where C is an integral constant.

\((\because\) \(\int\)sec²x dx = tan x and \(\int\)cosec²x dx = –cot x)

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