NTA Abhyas JEE Main2020MathematicsIndefinite IntegrationPractice
The value of ∫ t a n - 1 sin ⁡ x + 1 cos ⁡ x 3 + 2 sin ⁡ x - c o s 2 x d x is (where c is the constant of integration)
Options
- At a n - 1 sin x + c
- Bt a n - 1 sin x 2 + c
- Ct a n - 1 sin x + 1 2 2 + c
- Dt a n - 1 sin x 2 2 + c
Correct answer
C. t a n - 1 sin x + 1 2 2 + c
Step-by-step solution
Let, Ι = ∫ t a n - 1 sin ⁡ x + 1 cos ⁡ x 3 + 2 sin ⁡ x - 1 - s i n 2 x d x Substituting, 1 + sin ⁡ x = t ⇒ cos ⁡ x d x = d t Ι = ∫ t a n - 1 t d t 2 + t - 1 2 + 2 t - 1 Ι = ∫ t a n - 1 t d t 1 + t 2 Ι = t a n - 1 t 2 2 + c Ι = t a n - 1 sin ⁡ x + 1 2 2 + c