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JEE Main20199 Apr 2019Morning ShiftMathematicsIndefinite IntegrationActual

∫ s e c 2 x · cot 4 3 x d x is equal to

Options

  1. A3 t a n - 1 3 x + C
  2. B- 3 4 t a n - 4 3 x + C
  3. C- 3 t a n - 1 3 x + C
  4. D- 3 c o t - 1 3 x + C

Correct answer

C. - 3 t a n - 1 3 x + C

Step-by-step solution

Given integral can be written as I = ∫ sec 2 x tan x 4 3   d x Let tan x = t ⇒ sec 2 x d x = d t ⇒ I = ∫ t - 4 3   d t Using ∫ x n d x = x n + 1 n + 1 + C , we get I = t - 1 3 - 1 3 +   C ⇒ I = - 3 t 1 3 +   C ⇒ I = - 3 tan - 1 3 x + C .

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