MHT CET2016MathematicsIndefinite Integration
∫ x 2 + 2 a x + tan - 1 x x 2 + 1 d x = ________
Options
- Alog a ⋅ a x + tan - 1 x + c
- Bx + tan - 1 x log a + c
- Ca x + tan - 1 x log a + c
- Dlog a ⋅ x + tan - 1 x + c
Correct answer
C. a x + tan - 1 x log a + c
Step-by-step solution
I = ∫ ( x 2 + 2 ) a ( x + tan − 1 x ) x 2 + 1 d x = ∫ ( 1 + 1 x 2 + 1 ) e ( x + tan − 1 x ) ⋅ l n a d x Let ( x + tan − 1 x ) l n a = t ⇒ ( 1 + 1 1 + x 2 ) d x = d t l n a ⇒ I = ∫ e t l t l n a = e t l n a + C = a x + tan − 1 x l n a + C