What is the integral of xe^{x/3} ?

The integral of xe^{x/3} is 3e^{x/3}x-9e^{x/3}+C

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integral of xe^{x/3}

\int x e^{\frac{x}{3}} d x

3 e^{\frac{x}{3}} x - 9 e^{\frac{x}{3}} + C

Solution steps

\int x e^{\frac{x}{3}} d x

Apply Integration By Parts

: 3 e^{\frac{x}{3}} x - \int 3 e^{\frac{x}{3}} d x

= 3 e^{\frac{x}{3}} x - \int 3 e^{\frac{x}{3}} d x

\int 3 e^{\frac{x}{3}} d x = 9 e^{\frac{x}{3}}

= 3 e^{\frac{x}{3}} x - 9 e^{\frac{x}{3}}

Add a constant to the solution

= 3 e^{\frac{x}{3}} x - 9 e^{\frac{x}{3}} + C

\frac{d y}{d x}, sin (x + y) = 3 x - 2 y

\int \frac{4}{4 x + 1} d x

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

(t - 1) cos (4 (t - 1)) + t^{2}

f (x) = \frac{x ^{2}}{4 - cos ( x )}

What is the integral of xe^{x/3} ?
The integral of xe^{x/3} is 3e^{x/3}x-9e^{x/3}+C