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Manipal MET2012MathematicsIndefinite Integration

Evaluate (x-1) e^x (x+1)^3 d x

Options

  1. A0
  2. B(x+1)^2 e^x +C
  3. Ce^x (x+1)^2 +C
  4. De^x (x-1)^2 +(x+1)^2+C

Correct answer

C. e^x (x+1)^2 +C

Step-by-step solution

aligned Let & I= (x-1) e^x (x+1)^3 d x & I= x+1-2 (x+1)^3 e^x d x & = 1 (x+1)^2 - 2 (x+1)^3 e^x d x & e^x 1 (x+1)^2 d x-2 e^x 1 (x+1)^3 d x aligned Applying integrating by parts, we get aligned & array l = ( 1 (x+1)^2 e^x- e^x (-2) (x+1)^3 d x ) -2 e^x 1 (x+1)^3 d x = e^x (x+1)^2 +C array aligned Note We can use the formula e^x [f(x)+f^ (x) ] d x=e^x f(x)+C

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