Funktion $$$\frac{3500 \sqrt{255}}{867 x^{\frac{3}{2}}}$$$ integraali

Määritä $$$\int \frac{3500 \sqrt{255}}{867 x^{\frac{3}{2}}}\, dx$$$.

Sovella vakiokertoimen sääntöä $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ käyttäen $$$c=\frac{3500 \sqrt{255}}{867}$$$ ja $$$f{\left(x \right)} = \frac{1}{x^{\frac{3}{2}}}$$$:

$${\color{red}{\int{\frac{3500 \sqrt{255}}{867 x^{\frac{3}{2}}} d x}}} = {\color{red}{\left(\frac{3500 \sqrt{255} \int{\frac{1}{x^{\frac{3}{2}}} d x}}{867}\right)}}$$

Sovella potenssisääntöä $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ käyttäen $$$n=- \frac{3}{2}$$$:

$$\frac{3500 \sqrt{255} {\color{red}{\int{\frac{1}{x^{\frac{3}{2}}} d x}}}}{867}=\frac{3500 \sqrt{255} {\color{red}{\int{x^{- \frac{3}{2}} d x}}}}{867}=\frac{3500 \sqrt{255} {\color{red}{\frac{x^{- \frac{3}{2} + 1}}{- \frac{3}{2} + 1}}}}{867}=\frac{3500 \sqrt{255} {\color{red}{\left(- 2 x^{- \frac{1}{2}}\right)}}}{867}=\frac{3500 \sqrt{255} {\color{red}{\left(- \frac{2}{\sqrt{x}}\right)}}}{867}$$

Näin ollen,

$$\int{\frac{3500 \sqrt{255}}{867 x^{\frac{3}{2}}} d x} = - \frac{7000 \sqrt{255}}{867 \sqrt{x}}$$

Lisää integrointivakio:

$$\int{\frac{3500 \sqrt{255}}{867 x^{\frac{3}{2}}} d x} = - \frac{7000 \sqrt{255}}{867 \sqrt{x}}+C$$

$$$\int \frac{3500 \sqrt{255}}{867 x^{\frac{3}{2}}}\, dx = - \frac{7000 \sqrt{255}}{867 \sqrt{x}} + C$$$A