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AP EAMCET2008MathematicsIndefinite Integration

If I_n= x^n e^ c x d x for n 1, then c I_n+n I_ n-1 is equal to

Options

  1. Ax^n e^ c x
  2. Bx^n
  3. Ce^ c x
  4. Dx^n+e^ c x

Correct answer

A. x^n e^ c x

Step-by-step solution

Given that, aligned & I_n= x^n e^ c x d x & I_n= e^ c x c x^n- e^ c x c n x^ n-1 d x & I_n= e^ c x x^n c - n c I_ n-1 & aligned c I_n+n I_ n-1 =e^ c x x^n

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