AP EAMCET202018 Sep 2020Morning ShiftMathematicsIndefinite IntegrationActual
( [ ( x)+ 1 ( x)^2 ] d x= )
Options
- A(x[ ( x)+ x]+c )
- B( x ( x) +c )
- C(x ( x)+c )
- D(x [ ( x)- 1 x ]+c )
Correct answer
D. (x [ ( x)- 1 x ]+c )
Step-by-step solution
(I= [ ( x)+ 1 ( x)^2 ] d x ) Let, ( x=t d x=e^t d t ) ( I= e^t ( (t)+ 1 t^2 ) d t ) ( aligned & = e^t [ ( t+ 1 t )- ( 1 t - 1 t^2 ) ] d t & = e^t ( t+ 1 t ) d t- e^t ( 1 t - 1 t^2 ) d t aligned ) As, we know that, ( e^x (f(x)+f^ (x) ) d x= e^x f(x)+C , ) ( aligned So, I & =e^t t- e^t t +C & =x ( x)- x x +C t= x & =x [ ( x)- 1 x ]+C aligned )