$$$\frac{1}{256 x^{16}}$$$'nin integrali

Bulun: $$$\int \frac{1}{256 x^{16}}\, dx$$$.

Sabit katsayı kuralı $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$'i $$$c=\frac{1}{256}$$$ ve $$$f{\left(x \right)} = \frac{1}{x^{16}}$$$ ile uygula:

$${\color{red}{\int{\frac{1}{256 x^{16}} d x}}} = {\color{red}{\left(\frac{\int{\frac{1}{x^{16}} d x}}{256}\right)}}$$

Kuvvet kuralını $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ $$$n=-16$$$ ile uygulayın:

$$\frac{{\color{red}{\int{\frac{1}{x^{16}} d x}}}}{256}=\frac{{\color{red}{\int{x^{-16} d x}}}}{256}=\frac{{\color{red}{\frac{x^{-16 + 1}}{-16 + 1}}}}{256}=\frac{{\color{red}{\left(- \frac{x^{-15}}{15}\right)}}}{256}=\frac{{\color{red}{\left(- \frac{1}{15 x^{15}}\right)}}}{256}$$

Dolayısıyla,

$$\int{\frac{1}{256 x^{16}} d x} = - \frac{1}{3840 x^{15}}$$

İntegrasyon sabitini ekleyin:

$$\int{\frac{1}{256 x^{16}} d x} = - \frac{1}{3840 x^{15}}+C$$

$$$\int \frac{1}{256 x^{16}}\, dx = - \frac{1}{3840 x^{15}} + C$$$A