MHT CET202311 May 2023Evening ShiftMathematicsIndefinite IntegrationActual
x 2 (x^2+1 )- 2 (x^2+1 ) 2 (x^2+1 )+ 2 (x^2+1 ) d x=
Options
- A( ( x^2+1 2 ) )+ c , where c is a constant of integration.
- B( x^2+1 2 )+ c , where c is a constant of integration.
- C( ( x^2+1 2 ) )+ c , where c is a constant of integration.
- D2 (x^2+1 )+ c , where c is a constant of integration.
Correct answer
A. ( ( x^2+1 2 ) )+ c , where c is a constant of integration.
Step-by-step solution
aligned & Let I = x 2 (x^2+1 )- 2 (x^2+1 ) 2 (x^2+1 )+ 2 (x^2+1 ) d x & = x 2 (x^2+1 )-2 (x^2+1 ) (x^2+1 ) 2 x (x^2+1 )+2 (x^2+1 ) (x^2+1 ) d x & = x 1- (x^2+1 ) 1+ (x^2+1 ) d x & = x 2 ^2 ( x^2+1 2 ) 2 ^2 ( x^2+1 2 ) d x & = x ( x^2+1 2 ) d x & Let ( x^2+1 2 )= t x ~d x= dt & I = t d t & = ( t )+ c & = ( ( x^2+1 2 ) )+ c & aligned