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人気のある微分積分 >

integral of (6^{sqrt(x)})/(sqrt(x))

解

\int \frac{6 ^{x}}{x} d x

解

\frac{2 \cdot 6 ^{x}}{ln ( 6 )} + C

解答ステップ

\int \frac{6 ^{x}}{x} d x

u置換積分法を適用する

= \int 3^{u} \cdot 2^{u + 1} d u

簡素化

2^{u + 1} : 2^{u} \cdot 2

= \int 3^{u} \cdot 2^{u} \cdot 2 d u

定数を除く:

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

= 2 \cdot \int 3^{u} \cdot 2^{u} d u

簡素化

3^{u} \cdot 2^{u} : 6^{u}

= 2 \cdot \int 6^{u} d u

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

= 2 \cdot \frac{6 ^{u}}{ln ( 6 )}

代用を戻す

u = x

= 2 \cdot \frac{6 ^{x}}{ln ( 6 )}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 \cdot 6 ^{x}}{ln ( 6 )}

定数を解答に追加する

= \frac{2 \cdot 6 ^{x}}{ln ( 6 )} + C

グラフ

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