AP EAMCET201920 Apr 2019Evening ShiftMathematicsIndefinite IntegrationActual
1-x^2 ⁻¹ x+x 1-x^2 d x=
Options
- Ax ⁻¹ x+ 1-x^2 +c
- B⁻¹ x+ 1-x^2 +c
- Cx ⁻¹ x+c
- Dx ⁻¹ x 1-x^2 +c
Correct answer
C. x ⁻¹ x+c
Step-by-step solution
aligned & Given, 1-x^2 ⁻¹ x+x 1-x^2 d x & ( 1-x^2 ⁻¹ x 1-x^2 + x 1-x^2 ) d x & ( ⁻¹ x+ x 1-x^2 ) d x & ⁻¹ x d x+ x 1-x^2 d x & ⁻¹ x 1 d x- ( d d x ⁻¹ x 1 d x ) d x+ x 1-x^2 d x & [ By using by parts with f(x)= ⁻¹ x ; g(x)=1 ] & ⁻¹ x x- 1 1-x^2 x d x+ x 1-x^2 d x+c & x ⁻¹ x+c aligned Hence option (c) is correct.