Integral of $$$r^{m}$$$ with respect to $$$m$$$

The calculator will find the integral/antiderivative of $$$r^{m}$$$ with respect to $$$m$$$, with steps shown.

Find $$$\int r^{m}\, dm$$$.

Apply the exponential rule $$$\int{a^{m} d m} = \frac{a^{m}}{\ln{\left(a \right)}}$$$ with $$$a=r$$$:

$${\color{red}{\int{r^{m} d m}}} = {\color{red}{\frac{r^{m}}{\ln{\left(r \right)}}}}$$

Therefore,

$$\int{r^{m} d m} = \frac{r^{m}}{\ln{\left(r \right)}}$$

Add the constant of integration:

$$\int{r^{m} d m} = \frac{r^{m}}{\ln{\left(r \right)}}+C$$

$$$\int r^{m}\, dm = \frac{r^{m}}{\ln\left(r\right)} + C$$$A

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