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MHT CET2018MathematicsIndefinite Integration

∫ 1 sin ⁡ x . cos 2 ⁡ x d x =

Options

  1. Asec x + log ⁡ sec ⁡ x + tan ⁡ x + c
  2. Bsec x . tan ⁡ x + c
  3. Csec x + log ⁡ sec ⁡ x - tan ⁡ x + c
  4. Dsec x + log ⁡ cosec ⁡ x - cot ⁡ x + c

Correct answer

D. sec x + log ⁡ cosec ⁡ x - cot ⁡ x + c

Step-by-step solution

I = ∫ 1 sin x ⋅ cos 2 x I = ∫ sin 2 x + cos 2 x sin x ⋅ cos 2 x d x I = ∫ sin 2 x sin x ⋅ cos 2 x d x + ∫ cos 2 x d x sin x cos 2 x I = ∫ sec x tan x d x + ∫ cosec x d x I = sec x + ln | cosec x − cot x | + c

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