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NDA2020MathematicsIndefinite IntegrationActual

What is (e^ x + x ) x d x equal to ?

Options

  1. Ax+x x+ ^2 x 2 +c
  2. Bx-x x+ ^2 x 2 +c
  3. Cx x+ x+ ^2 x 2 +c
  4. Dx x-x x+ ^2 x 2 +c

Correct answer

C. x x+ x+ ^2 x 2 +c

Step-by-step solution

aligned & (e^ x + x ) x d x= (x+ x) x d x & = (x x+ x x) d x aligned aligned & = x x d x+ x x d x & =x x d x- ( d x d x ( x) d x ) d x & + x x d x aligned aligned & =x x- x d x+ x x d x & =x x-(- x)+ x x d x aligned =x x+ x+ x x d x Now, x x d x Let x=z, d z= x d x x x d x= z d z= z^2 2 = ^2 x 2 I=x x+ x+ ^2 x 2 +C

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