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NDA2010MathematicsIndefinite IntegrationActual

What is equal to? e^x(1+x) ^2 (x e^x ) d x where c is a constant of integration.

Options

  1. Ax e^x+c
  2. B(x e^x )+c
  3. C(x e^x )+c
  4. Dx cosec (x e^x )+c

Correct answer

C. (x e^x )+c

Step-by-step solution

aligned & e^x(1+x) ^2 (x e^x ) d x & Put x e^x=z & e^x(1+x) d x=d z & d z ^2 z = ^2 z d z= z+c & = (x e^x )+c aligned

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