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人気のある微分積分 >

integral of 2^x2^{2^x}

解

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

解

\frac{1}{ln ^{2} ( 2 )} \cdot 2^{2^{x}} + C

解答ステップ

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

u置換積分法を適用する

= \int \frac{2 ^{u}}{ln ( 2 )} d u

定数を除く:

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

= \frac{1}{ln ( 2 )} \cdot \int 2^{u} d u

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

= \frac{1}{ln ( 2 )} \cdot \frac{2 ^{u}}{ln ( 2 )}

代用を戻す

u = 2^{x}

= \frac{1}{ln ( 2 )} \cdot \frac{2 ^{2^{x}}}{ln ( 2 )}

簡素化

\frac{1}{ln ( 2 )} \cdot \frac{2 ^{2^{x}}}{ln ( 2 )} : \frac{1}{ln ^{2} ( 2 )} \cdot 2^{2^{x}}

= \frac{1}{ln ^{2} ( 2 )} \cdot 2^{2^{x}}

定数を解答に追加する

= \frac{1}{ln ^{2} ( 2 )} \cdot 2^{2^{x}} + C

グラフ

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