What is the integral of 5xe^{-x} ?

The integral of 5xe^{-x} is 5(-e^{-x}x-e^{-x})+C

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integral of 5xe^{-x}

\int 5 x e^{- x} d x

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

Solution steps

\int 5 x e^{- x} d x

Take the constant out:

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

= 5 \cdot \int x e^{- x} d x

Apply Integration By Parts

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

= 5 (- e^{- x} x - \int - e^{- x} d x)

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

= 5 (- e^{- x} x - e^{- x})

Add a constant to the solution

= 5 (- e^{- x} x - e^{- x}) + C

y = (x^{2} + 1)^{2}

x y = - 64, (8, - 8)

\int \frac{1}{1 0 ^{x} + 1} d x

\frac{d}{d x} (10 cos (30 x - 7))

\int csch^{2} (13 x - \frac{4}{9}) d x

What is the integral of 5xe^{-x} ?
The integral of 5xe^{-x} is 5(-e^{-x}x-e^{-x})+C