What is the integral of-e^{-x}2x ?

The integral of-e^{-x}2x is -2(-e^{-x}x-e^{-x})+C

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integral of-e^{-x}2x

\int - e^{- x} 2 x d x

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

Solution steps

\int - e^{- x} \cdot 2 x d x

Take the constant out:

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

= - 2 \cdot \int e^{- x} x d x

Apply Integration By Parts

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

= - 2 (- e^{- x} x - \int - e^{- x} d x)

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

= - 2 (- e^{- x} x - e^{- x})

Add a constant to the solution

= - 2 (- e^{- x} x - e^{- x}) + C

y = 2 t (3 t^{2} - 5)^{3}

\int \frac{5 sin ( x ) + 4 sec ( x )}{tan ( x )} d x

\frac{d}{d x} (e^{x} (x^{2} + 5 x))

\frac{d}{d x} (x 3 x - 2)

x y^{^{'}} + y = 0, y (4) = 6

What is the integral of-e^{-x}2x ?
The integral of-e^{-x}2x is -2(-e^{-x}x-e^{-x})+C