integral of x^{10}+10^x

解

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

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

解答ステップ

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

総和規則を適用する:

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

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

定数を解答に追加する

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