MHT CET202616 April 2026Morning ShiftMathematicsIndefinite IntegrationActual
^3 x ^2 x + x ,dx =
Options
- A( x) + x + c , where c is the constant of integration
- B( x) - x + c , where c is the constant of integration
- C( x) + x + c , where c is the constant of integration
- D( x) - x + c , where c is the constant of integration
Correct answer
B. ( x) - x + c , where c is the constant of integration
Step-by-step solution
Let I = ^3 x ^2 x + x ,dx We can write ^3 x = ^2 x x = (1 - ^2 x) x I = 1 - ^2 x ^2 x + x x ,dx Let x = t , then x ,dx = dt Substituting these into the integral, we get: I = 1 - t^2 t^2 + t ,dt I = (1 - t)(1 + t) t(t + 1) ,dt I = 1 - t t ,dt I = ( 1 t - 1 ) ,dt I = (t) - t + c Substituting back t = x , we get: I = ( x) - x + c Answer: ( x) - x + c , where c is the constant of integration