KCET2011MathematicsIndefinite Integration
When x>0 , then ¹ ( 1-x² 1+x² ) d x is
Options
- A2 [x ¹ x- (1+x² ) ]+C
- B2 [x ¹ x+ (1+x² ) ]+C
- C2 x ⁻¹ x+ (1+x² )+C
- D2 x ⁻¹ x- (1+x² )+C
Correct answer
D. 2 x ⁻¹ x- (1+x² )+C
Step-by-step solution
Given, when x>0 = ¹ ( 1-x² 1+x² ) d x [ array l x>0 2 ⁻¹ x= ⁻¹ ( 1-x² 1+x² ) array ]= 2 ⁻¹ x d x=2 1 II ⁻¹ x d x=2 x ⁻¹ x- 1 1+x² x d x =2 x ⁻¹ x- 2 x 1+x² d x=2 x ⁻¹ x- (1+x² )+C