AP EAMCET202018 Sep 2020Evening ShiftMathematicsIndefinite IntegrationActual
( e^ x / 2 ( 2+ x 1+ x ) d x= )
Options
- A(2 e^ x / 2 cosec ( x 2 )+c )
- B(2 e^ x / 2 ( x 2 )+c )
- C(2 e^ x / 2 ( x 2 )+c )
- D(2 e^ x / 2 ( x 2 )+c )
Correct answer
B. (2 e^ x / 2 ( x 2 )+c )
Step-by-step solution
( aligned & e^ x 2 ( 2+ x 1+ x ) d x & e^ x 2 ( 2+ 2 x / 2 1+ ^2 x / 2 1+ 1- ^2 x / 2 1+ ^2 x / 2 ) d x & e^ x 2 ( 2+2 ^2 x / 2+2 x / 2 1+ ^2 x / 2+1- ^2 x / 2 ) d x aligned ) ( gathered e^ x 2 2 ( 1+ ^2 x / 2+ x / 2 2 ) d x e^ x 2 ( ^2 x 2 + x 2 ) d x Put, x 2 =t d x=2 d t e^t ( ^2 t+ t ) 20 d t 2 e^t t+c 2 e^ x 2 x 2 +c gathered ) Hence, option (b) is correct.