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人気のある微分積分 >

integral of (x*9^{2x^2-8})

解

\int (x \cdot 9^{2 x^{2} - 8}) d x

解

\frac{3 ^{4 x^{2} - 16}}{8 ln ( 3 )} + C

解答ステップ

\int x \cdot 9^{2 x^{2} - 8} d x

x 9^{2 x^{2} - 8} = 9^{- 8} x 9^{2 x^{2}}

= \int 9^{- 8} x \cdot 9^{2 x^{2}} d x

定数を除く:

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

= 9^{- 8} \cdot \int x \cdot 9^{2 x^{2}} d x

9^{- 8} = \frac{1}{43046721}

= \frac{1}{43046721} \cdot \int x \cdot 9^{2 x^{2}} d x

u置換積分法を適用する

= \frac{1}{43046721} \cdot \int \frac{8 1 ^{u}}{2} d u

定数を除く:

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

= \frac{1}{43046721} \cdot \frac{1}{2} \cdot \int 8 1^{u} d u

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

= \frac{1}{43046721} \cdot \frac{1}{2} \cdot \frac{8 1 ^{u}}{ln ( 81 )}

代用を戻す

u = x^{2}

= \frac{1}{43046721} \cdot \frac{1}{2} \cdot \frac{8 1 ^{x^{2}}}{ln ( 81 )}

簡素化

\frac{1}{43046721} \cdot \frac{1}{2} \cdot \frac{8 1 ^{x^{2}}}{ln ( 81 )} : \frac{3 ^{4 x^{2} - 16}}{8 ln ( 3 )}

= \frac{3 ^{4 x^{2} - 16}}{8 ln ( 3 )}

定数を解答に追加する

= \frac{3 ^{4 x^{2} - 16}}{8 ln ( 3 )} + C

グラフ

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