What is the integral of 5xe^x ?

The integral of 5xe^x is 5(e^xx-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

\int_{\frac{π}{6}}^{\frac{π}{4}} tan (x) d x

\frac{1}{s ^{4} ( s ^{2} - 4 )}

y^{2} - 4 x = 4, 4 x - y = 16

x \to 1 lim (7 - 2 x - x^{2})

\frac{d}{d x} ((\frac{- sin ( x )}{1 - cos ( x )})^{2})