What is the integral of xe^{B-x} ?

The integral of xe^{B-x} is e^B(-e^{-x}x-e^{-x})+C

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integral of xe^{B-x}

\int x e^{B - x} d x

e^{B} (- e^{- x} x - e^{- x}) + C

Solution steps

\int x e^{B - x} d x

Simplify

e^{B - x} : e^{B} e^{- x}

= \int x e^{B} e^{- x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{B} \cdot \int x e^{- x} d x

Apply Integration By Parts

= e^{B} (- e^{- x} x - \int - e^{- x} d x)

\int - e^{- x} d x = e^{- x}

= e^{B} (- e^{- x} x - e^{- x})

Add a constant to the solution

= e^{B} (- e^{- x} x - e^{- x}) + C

x \to \infty lim (\frac{5}{0})

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = 1

\frac{d y}{d x} = 4 y + 3 e^{8 x} (x + 1)

\int \frac{r}{1 + r ^{2}} d r

\int \frac{e ^{x}}{1 + 49 e ^{2 x}} d x

What is the integral of xe^{B-x} ?
The integral of xe^{B-x} is e^B(-e^{-x}x-e^{-x})+C