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NTA Abhyas JEE Main2020MathematicsIndefinite IntegrationPractice

The integral I = ∫ sec 3 ⁡ x tan 3 ⁡ x d x is equal to (where, C is the constant of integration)

Options

  1. Asec 5 ⁡ x - sec 3 ⁡ x + C
  2. Bsec 5 ⁡ x 5 - sec 3 ⁡ x + C
  3. Csec 5 ⁡ x 5 - sec 3 ⁡ x 3 + C
  4. Dsec 5 ⁡ x 5 - tan - 1 ⁡ x + C

Correct answer

C. sec 5 ⁡ x 5 - sec 3 ⁡ x 3 + C

Step-by-step solution

Let sec ⁡ x = t ⇒ sec ⁡ x tan ⁡ x d x = d t ∴ I = ∫ sec 2 ⁡ x tan 2 ⁡ x sec x tan x d x = ∫ t 2 t 2 - 1 d t = ∫ t 4 - t 2 d t = t 5 5 - t 3 3 + C I = sec 5 ⁡ x 5 - sec 3 ⁡ x 3 + C

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