Integral of $$$u^{\frac{11}{4}}$$$

Find $$$\int u^{\frac{11}{4}}\, du$$$.

Apply the power rule $$$\int u^{n}\, du = \frac{u^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=\frac{11}{4}$$$:

$${\color{red}{\int{u^{\frac{11}{4}} d u}}}={\color{red}{\frac{u^{1 + \frac{11}{4}}}{1 + \frac{11}{4}}}}={\color{red}{\left(\frac{4 u^{\frac{15}{4}}}{15}\right)}}$$

Therefore,

$$\int{u^{\frac{11}{4}} d u} = \frac{4 u^{\frac{15}{4}}}{15}$$

Add the constant of integration:

$$\int{u^{\frac{11}{4}} d u} = \frac{4 u^{\frac{15}{4}}}{15}+C$$

$$$\int u^{\frac{11}{4}}\, du = \frac{4 u^{\frac{15}{4}}}{15} + C$$$A