What is the integral of 3xe^{-x} ?

The integral of 3xe^{-x} is 3(-e^{-x}x-e^{-x})+C

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integral of 3xe^{-x}

\int 3 x e^{- x} d x

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

Solution steps

\int 3 x e^{- x} d x

Take the constant out:

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

= 3 \cdot \int x e^{- x} d x

Apply Integration By Parts

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

= 3 (- e^{- x} x - \int - e^{- x} d x)

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

= 3 (- e^{- x} x - e^{- x})

Add a constant to the solution

= 3 (- e^{- x} x - e^{- x}) + C

\int (y + 1)^{2} d y

x \to 0 lim (\frac{e ^{8 x} - 1}{x})

(2, 1), (- 4, - 2)

\int 4 x^{2} cos (\frac{x}{5}) d x

x \to 3 - lim (\frac{2}{( x - 3 ) ^{3}})

What is the integral of 3xe^{-x} ?
The integral of 3xe^{-x} is 3(-e^{-x}x-e^{-x})+C