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NDA2015MathematicsIndefinite IntegrationActual

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

Options

  1. A(x+1)^2 e^x+c
  2. B(x+1) e^x+c
  3. Ce^x x+1 +c
  4. De^x (x+1)^2 +c

Correct answer

C. e^x x+1 +c

Step-by-step solution

aligned & x e^x (1+x)^2 d x & = e^x [ 1 1+x - 1 (1+x)^2 ] d x & = e^x 1+x +C e^x (f(x)+f^ (x) ) d x=e^x f(x) aligned

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