AP EAMCET2016MathematicsIndefinite Integration
If (a^2+x^2 ) d x=h(x)+C , then h (x) is equal to
Options
- Ax (a^2+x^2 )+2 ⁻¹ ( x a )
- Bx^2 (a^2+x^2 )+x+a ⁻¹ ( x a )
- Cx (a^2+x^2 )-2 x+2 a ⁻¹ ( x a )
- Dx^2 (a^2+x^2 )+2 x-a^2 ⁻¹ ( x a )
Correct answer
C. x (a^2+x^2 )-2 x+2 a ⁻¹ ( x a )
Step-by-step solution
Let l= (a^2+x^2 ) d x By using method of integration by parts, we get = (a^2+x^2 ) d x- d ( (a^2+x^2 ) . d x d x d x+C aligned & = (a^2+x^2 ) 2 x x^2+a^2 x d x+C & =x (a^2+x^2 )-2 x^2 x^2+a^2 d x+C & =x (a^2+x^2 )-2 x^2+a^2 x^2+a^2 d x+2 a^2 x^2+a^2 d x & =x (a^2+x^2 )- 2 a^2 a ⁻¹ x a +C & l=x (a^2+x^2 )-2 x+2 a ⁻¹ x a +C aligned Comparing the above equation with (x^2+a^2 ) d x=h(x)+ C , we get h(x)=x (a^2+x^2 )-2 x+2 a ⁻¹ ( x a )