MHT CET202124 Sep 2021Evening ShiftMathematicsIndefinite IntegrationActual
e^x ( 1+ x 1+ x ) d x=
Options
- Ae ^ x x 2 + c
- Be^x x 2 +c
- Ce ^ x x 2 + c
- De^x x 2 +c
Correct answer
A. e ^ x x 2 + c
Step-by-step solution
aligned & I= e^x ( 1+ x 1+ x ) d x= e^x ( 1 1+ x + x 1+ x ) d x & = e^x ( 1 2 ^2 x 2 + 2 x 2 x 2 2 ^2 x 2 ) d x= e^x ( 1 2 ) ( ^2 x 2 +2 x 2 ) d x & = 1 2 e^x [2 x 2 + ^2 x 2 ] d x= 1 2 e^x(2)+ ( x 2 )+c=e^x x 2 +c aligned