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AP EAMCET202018 Sep 2020Evening ShiftMathematicsIndefinite IntegrationActual

( [ 1 x - 1 ( x)^2 ] d x= )

Options

  1. A(x x+c )
  2. B(-x x+c )
  3. C( x x +c )
  4. D( x x +c )

Correct answer

D. ( x x +c )

Step-by-step solution

( ( 1 x - 1 ( x)^2 ) d x ) Put, ( x=t ) ( array l x=e^t d x=e^t d t ( 1 t + -1 t^2 ) e^t d t array ) We have, ( aligned e^x (f(x)+f^ (x) d x . & .=e^x f(x)+C ) & =e^t 1 t +c= e^ x x +c= x x +c aligned ) Hence, option (d) is correct.

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