Integralen av $$$\frac{9}{949 x^{4}}$$$

Bestäm $$$\int \frac{9}{949 x^{4}}\, dx$$$.

Tillämpa konstantfaktorregeln $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ med $$$c=\frac{9}{949}$$$ och $$$f{\left(x \right)} = \frac{1}{x^{4}}$$$:

$${\color{red}{\int{\frac{9}{949 x^{4}} d x}}} = {\color{red}{\left(\frac{9 \int{\frac{1}{x^{4}} d x}}{949}\right)}}$$

Tillämpa potensregeln $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ med $$$n=-4$$$:

$$\frac{9 {\color{red}{\int{\frac{1}{x^{4}} d x}}}}{949}=\frac{9 {\color{red}{\int{x^{-4} d x}}}}{949}=\frac{9 {\color{red}{\frac{x^{-4 + 1}}{-4 + 1}}}}{949}=\frac{9 {\color{red}{\left(- \frac{x^{-3}}{3}\right)}}}{949}=\frac{9 {\color{red}{\left(- \frac{1}{3 x^{3}}\right)}}}{949}$$

Alltså,

$$\int{\frac{9}{949 x^{4}} d x} = - \frac{3}{949 x^{3}}$$

Lägg till integrationskonstanten:

$$\int{\frac{9}{949 x^{4}} d x} = - \frac{3}{949 x^{3}}+C$$

$$$\int \frac{9}{949 x^{4}}\, dx = - \frac{3}{949 x^{3}} + C$$$A