NTA Abhyas JEE Main2020MathematicsIndefinite IntegrationPractice

∫ sin 4 ⁡ x cos 8 ⁡ x d x is equal to (where C is an arbitrary constant)

Options

A1 + tan 5 ⁡ x 5 + tan 5 ⁡ x 7 + C
Btan 5 ⁡ x 5 + tan 7 ⁡ x 7 + C
Ctan 7 ⁡ x 5 + tan 5 ⁡ x 7 + C
DNone of these

Correct answer

B. tan 5 ⁡ x 5 + tan 7 ⁡ x 7 + C

Step-by-step solution

∫ sin 4 ⁡ x cos 4 ⁡ x cos 8 ⁡ x cos 4 ⁡ x . d x = ∫ tan 4 ⁡ x . sec 4 ⁡ x d x = ∫ tan 4 ⁡ x 1 + tan 2 ⁡ x sec 2 ⁡ x d x = ∫ tan 4 ⁡ x 1 + tan 2 ⁡ x d tan x = ∫ t 4 1 + t 2 dt= t 5 5 + t 7 7 + C

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