MHT CET2019Morning ShiftMathematicsIndefinite IntegrationActual
∫ d x s i n x + c o s x 2 c o s x + s i n x =
Options
- Alog s i n x + c o s x + c
- Blog t a n x + 2 t a n x + 1 + c
- Clog s i n x + c o s x 2 c o s x - s i n x + c
- Dlog t a n x + 1 t a n x + 2 + c
Correct answer
D. log t a n x + 1 t a n x + 2 + c
Step-by-step solution
Let l = ∫ d x s i n x + c o s x 2 c o s x + s i n x = ∫ s e c 2 x t a n x + 1 2 + t a n x d x Put t a n x = t ⇒ s e c 2 x d x = d t ∫ d t t + 1 t + 2 H e r e , 1 t + 1 t + 2 = A t + 1 + B t + 2 ⇒ 1 = A t + 2 + B t + 1 Put t = - 2 ∴ 1 = B - 1 ⇒ B = - 1 ∴ P u t t + 1 = 0 ⇒ t = - 1 ∴ 1 = A 1 ⇒ A = 1 N o w , ∫ d t t + 1 t + 2 = ∫ 1 t + 1 d t = - ∫ 1 t + 2 d t = log t + 1 - log t + 2 + C = log t + 1 t + 2 + C = log t a n x + 1 t a n x + 2 + C