Manipal MET2013MathematicsIndefinite Integration
1+ cosec x d x is equal to
Options
- A⁻¹( x- x)+c
- B2 ⁻¹( x)+c
- C⁻¹ ( x 2 - x 2 )+c
- D2 ⁻¹ ( x 2 - x 2 )+c
Correct answer
D. 2 ⁻¹ ( x 2 - x 2 )+c
Step-by-step solution
Let I= 1+ cosec x d x= 1+ x x d x= x 2 + x 2 2 x 2 x 2 d x= x 2 + x 2 1- ( x 2 - x 2 )^2 d x Put, x 2 - x 2 =t ( x 2 + x 2 ) d x=2 d t I= 2 d t 1-t^2 = 2 ⁻¹ t+c= 2 ⁻¹ ( x 2 - x 2 )+c