What is the integral of re^{r/3} ?

The integral of re^{r/3} is 3e^{r/3}r-9e^{r/3}+C

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integral of re^{r/3}

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (x^{2} + y^{2} - y^{2} x - 2)

x \to \infty + lim (x^{3})

x \to 0 - lim (18 - \frac{4}{x ^{3}})

\frac{d}{d x} (e^{x s i n h (x)})

x \to \infty lim (2 x + 3)

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