MHT CET202410 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
1+ ( x) 1+ ( x) d x=
Options
- Ax^2 ( x 2 )+ c , where c is a constant of integration.
- Bx ( ( x 2 ) )+ c , where c is a constant of integration.
- Cx^3 ( x 2 )+ c , where c is a constant of
- Dx ( x 2 )+ c , where c is a constant of integration.
Correct answer
D. x ( x 2 )+ c , where c is a constant of integration.
Step-by-step solution
aligned & I = 1+ ( x) 1+ ( x) d x & Put x= t & x= e ^ t & ~d x= e ^ t dt & I= ( 1+ t 1+ t ) e^t d t & I= ( ^2 t 2 + ^2 t 2 +2 t 2 t 2 2 ^2 t 2 ) e ^ t dt & = 1 2 ( ^2 t 2 +1+2 t 2 ) e ^ t dt & = 1 2 ( ^2 t 2 +2 t 2 ) e^t d t & = 1 2 2 t 2 e ^ t + C & [ e ^x [ f (x)+ f ^ (x) ] d x= e ^x f (x)+ c ] . & = t 2 e^t+c aligned I= ( x 2 ) x+c