Indefinite IntegrationHard

Question

The value of dx is equal to

Options

A. ln2 (cot x) + C
B.ln2 (sec x) + C
C.ln2 (sin x sec x) + C
D.ln2 (cos x cosec x) + C

Solution

I = dx      put ln tanx = t ⇒ dx = dt
∴ I = = (ln cot x)2 + C = (ln2 cot x) + C
= ln2 (sin x sec x) + C = ln2 (cos x cosec x) + C

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