Integralen av $$$310 x^{34}$$$

Bestäm $$$\int 310 x^{34}\, dx$$$.

Tillämpa konstantfaktorregeln $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ med $$$c=310$$$ och $$$f{\left(x \right)} = x^{34}$$$:

$${\color{red}{\int{310 x^{34} d x}}} = {\color{red}{\left(310 \int{x^{34} d x}\right)}}$$

Tillämpa potensregeln $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ med $$$n=34$$$:

$$310 {\color{red}{\int{x^{34} d x}}}=310 {\color{red}{\frac{x^{1 + 34}}{1 + 34}}}=310 {\color{red}{\left(\frac{x^{35}}{35}\right)}}$$

Alltså,

$$\int{310 x^{34} d x} = \frac{62 x^{35}}{7}$$

Lägg till integrationskonstanten:

$$\int{310 x^{34} d x} = \frac{62 x^{35}}{7}+C$$

$$$\int 310 x^{34}\, dx = \frac{62 x^{35}}{7} + C$$$A