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MHT CET202411 May 2024Evening ShiftMathematicsIndefinite IntegrationActual

If f (x)=1+x ; g (x)= x , then g ( f (x)) d x is equal to

Options

  1. A(1+x) (1+x)-x+ c , (where c is a constant of integration)
  2. B(1+x) x-x+ c , (where c is a constant of integration)
  3. Cx (1+x)+ c , (where c is a constant of integration)
  4. D(1+x) (1+x)+x+ c , (where c is a constant of integration)

Correct answer

A. (1+x) (1+x)-x+ c , (where c is a constant of integration)

Step-by-step solution

aligned & g ( f (x)) d x & = 1 (1+x) d x aligned aligned & =x (1+x)- x 1 (1+x) d x+ c & =x (1+x)- [ 1+x 1+x ~d x- 1 1+x ~d x ]+ c & =x (1+x)-x+ (1+x)+ c & =(1+x) (1+x)-x+ c aligned

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