What is the integral of 7xe^{-x} ?

The integral of 7xe^{-x} is 7(-e^{-x}x-e^{-x})+C

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integral of 7xe^{-x}

\int 7 x e^{- x} d x

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

Solution steps

\int 7 x e^{- x} d x

Take the constant out:

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

= 7 \cdot \int x e^{- x} d x

Apply Integration By Parts

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

= 7 (- e^{- x} x - \int - e^{- x} d x)

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

= 7 (- e^{- x} x - e^{- x})

Add a constant to the solution

= 7 (- e^{- x} x - e^{- x}) + C

x \to 2 lim (1)

4 (ln (y)) y^{^{'}} - x^{9} y = 0

\frac{\partial}{\partial s} (t e^{s t})

\int (t^{3}) (e^{- 2 t}) d t

\frac{d y}{d x} = x^{2} - y - 2

What is the integral of 7xe^{-x} ?
The integral of 7xe^{-x} is 7(-e^{-x}x-e^{-x})+C