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