AP EAMCET2005MathematicsIndefinite Integration
If ⁻¹ ( 2 x 1+x^2 ) d x=f(x)- (1+x^2 ) then f(x) is equal to
Options
- A2 x ⁻¹ x
- B-2 x ⁻¹ x
- Cx ⁻¹ x
- D-x ⁻¹ x
Correct answer
A. 2 x ⁻¹ x
Step-by-step solution
Let I= ⁻¹ ( 2 x 1+x^2 ) d x Put x= d x= ^2 d aligned I & = ⁻¹( 2 ) ^2 d & =2 ^2 d & =2 [ - d ] & =2[ + ]+c & =2 [x ⁻¹ x+ 1 1+x^2 ]+c & =2 x ⁻¹ x- (1+x^2 )+c aligned But I=f(x)- (1+x^2 )+c array cc & f(x)- (1+x^2 )+c & =2 x ⁻¹ x- (1+x^2 )+c & f(x)=2 x ⁻¹ x array