What is the integral of 6xe^{-x} ?

The integral of 6xe^{-x} is 6(-e^{-x}x-e^{-x})+C

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integral of 6xe^{-x}

\int 6 x e^{- x} d x

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

Solution steps

\int 6 x e^{- x} d x

Take the constant out:

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

= 6 \cdot \int x e^{- x} d x

Apply Integration By Parts

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

= 6 (- e^{- x} x - \int - e^{- x} d x)

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

= 6 (- e^{- x} x - e^{- x})

Add a constant to the solution

= 6 (- e^{- x} x - e^{- x}) + C

\int \frac{1}{sin ( x ) cos ^{5} ( x )} d x

\frac{d}{d x} (x (x - 7)^{2})

ln (7 - 3 x), 2

\frac{d}{d x} (\frac{7}{4 - 3 x})

\frac{d}{d x} (cos^{2} (a - x))

What is the integral of 6xe^{-x} ?
The integral of 6xe^{-x} is 6(-e^{-x}x-e^{-x})+C