MHT CET202410 May 2024Evening ShiftMathematicsIndefinite IntegrationActual
⁻¹ ( 2 x 1+x^2 ) d x=
Options
- A2 x ⁻¹ x- (1+x^2 )+ c , where c is a constant of integration.
- B2 (x ⁻¹ x- (1+x^2 ) )+ c , where c is a constant of integration.
- Cx ⁻¹ x+ (1+x^2 )+ c , where c is a . constant of integration.
- D2 (x ⁻¹ x+ (1+x^2 ) )+ c , where c is a constant of integration.
Correct answer
A. 2 x ⁻¹ x- (1+x^2 )+ c , where c is a constant of integration.
Step-by-step solution
array ll & I= ⁻¹ ( 2 x 1+x^2 ) d x & Let x= t & d x= ^2 t d t array aligned I & = ⁻¹ ( 2 t 1+ ^2 t ) ^2 t dt & = ( ⁻¹( 2 t ) ^2 t ) dt & = 2 t ^2 t d t & =2 [ t ^2 t d t - dt dt ( ^2 t d dt ) dt ]+ c & =2 [ t t - t dt ]+ c & =2 t t +2 | t |+ c & =2 x ⁻¹ x+2 | 1 1+x^2 |+ c & =2 x ⁻¹ x- (1+x^2 )+ c aligned