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

The integral of 5xe^{x/5} is 5(5e^{x/5}x-25e^{x/5})+C

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integral of 5xe^{x/5}

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

5 (5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}}) + C

Solution steps

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

Apply Integration By Parts

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

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

\int 5 e^{\frac{x}{5}} d x = 25 e^{\frac{x}{5}}

= 5 (5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}})

Add a constant to the solution

= 5 (5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}}) + C

\int (sec^{2} (x) + 3) d x

\frac{d}{d x} (\frac{( 3 x + 3 )}{4 e ^{x}})

\int e x d x

y^{^{''}} + 4 y^{^{'}} + 4 y = 0

\frac{d}{d x} (\frac{24}{( 1 - x ) ^{5}})

What is the integral of 5xe^{x/5} ?
The integral of 5xe^{x/5} is 5(5e^{x/5}x-25e^{x/5})+C