Integral of $$$\frac{1}{x^{\frac{7}{10}}}$$$

Find $$$\int \frac{1}{x^{\frac{7}{10}}}\, dx$$$.

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=- \frac{7}{10}$$$:

$${\color{red}{\int{\frac{1}{x^{\frac{7}{10}}} d x}}}={\color{red}{\int{x^{- \frac{7}{10}} d x}}}={\color{red}{\frac{x^{- \frac{7}{10} + 1}}{- \frac{7}{10} + 1}}}={\color{red}{\left(\frac{10 x^{\frac{3}{10}}}{3}\right)}}$$

Therefore,

$$\int{\frac{1}{x^{\frac{7}{10}}} d x} = \frac{10 x^{\frac{3}{10}}}{3}$$

Add the constant of integration:

$$\int{\frac{1}{x^{\frac{7}{10}}} d x} = \frac{10 x^{\frac{3}{10}}}{3}+C$$

$$$\int \frac{1}{x^{\frac{7}{10}}}\, dx = \frac{10 x^{\frac{3}{10}}}{3} + C$$$A