d x ^ 2 x ^ 2 x equals - Vidyadip

Question

$\int \frac{d x}{\sin ^{2} x \cos ^{2} x}$ equals

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Answer

Let I = $\int \frac{d x}{\sin ^{2} x \cos ^{2} x}=\int \frac{1}{\sin ^{2} x \cos ^{2} x} d x$
$=\int \frac{\sin ^{2} x+\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x~~~$
$=\int \frac{\sin ^{2} x}{\sin ^{2} x \cos ^{2} x} d x+\int \frac{\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x$
$= \int \sec ^{2} x d x+\int cosec ^{2} x d x$
$$= tanx - cotx + C

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