integral of (x^{10}+10^x)/(10)

Lösung

\int \frac{x ^{10} + 1 0 ^{x}}{10} d x

\frac{1}{10} (\frac{x ^{11}}{11} + \frac{1 0 ^{x}}{ln ( 10 )}) + C

Schritte zur Lösung

\int \frac{x ^{10} + 1 0 ^{x}}{10} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{10} \cdot \int x^{10} + 1 0^{x} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{10} (\int x^{10} d x + \int 1 0^{x} d x)

\int x^{10} d x = \frac{x ^{11}}{11}

\int 1 0^{x} d x = \frac{1 0 ^{x}}{ln ( 10 )}

= \frac{1}{10} (\frac{x ^{11}}{11} + \frac{1 0 ^{x}}{ln ( 10 )})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{10} (\frac{x ^{11}}{11} + \frac{1 0 ^{x}}{ln ( 10 )}) + C

\frac{d}{d x} (\frac{5 x}{x ^{2} + 7})

x \to 0 lim (\frac{x}{2 x})

\int_{0}^{\frac{π}{6}} 1 - cos (6 x) d x

d er i v a t i v e y = 3 1 + 5 x

\int \frac{5 + x + x ^{2}}{x} d x