integral of 5^{2x}2

解

\int 5^{2 x} 2 d x

\frac{2 5 ^{x}}{ln ( 5 )} + C

解答ステップ

\int 5^{2 x} \cdot 2 d x

定数を除く:

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

= 2 \cdot \int 5^{2 x} d x

簡素化

5^{2 x} : 2 5^{x}

= 2 \cdot \int 2 5^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= 2 \cdot \frac{2 5 ^{x}}{ln ( 25 )}

簡素化

2 \cdot \frac{2 5 ^{x}}{ln ( 25 )} : \frac{2 5 ^{x}}{ln ( 5 )}

= \frac{2 5 ^{x}}{ln ( 5 )}

定数を解答に追加する

= \frac{2 5 ^{x}}{ln ( 5 )} + C