MHT CET2017MathematicsIndefinite Integration
If ∫ 1 x 2 + 4 x 2 + 9 d x = A tan - 1 x 2 + B tan - 1 x 3 + C then A - B =
Options
- A1 6
- B1 30
- C- 1 30
- D- 1 6
Correct answer
A. 1 6
Step-by-step solution
Since 1 A B = 1 B - A 1 A - 1 B ⇒ ∫ 1 x 2 + 4 x 2 + 9 d x = ∫ 1 5 1 x 2 + 4 - 1 x 2 + 9 d x = 1 5 1 2 tan - 1 x 2 - 1 3 tan - 1 x 3 + C ⇒ A = 1 10 B = - 1 15 ⇒ A − B = 1 10 + 1 15 = 5 30 = 1 6