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人気のある微分積分 >

integral from 1 to 4 of 3^{3x}

解

\int_{1}^{4} 3^{3 x} d x

解

\frac{177138}{ln ( 3 )}

+1

十進法表記

161237.95612 \dots

解答ステップ

\int_{1}^{4} 3^{3 x} d x

簡素化

3^{3 x} : 2 7^{x}

= \int_{1}^{4} 2 7^{x} d x

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

= [\frac{2 7 ^{x}}{ln ( 27 )}]_{1}^{4}

\frac{2 7 ^{x}}{ln ( 27 )} = \frac{3 ^{3 x - 1}}{ln ( 3 )}

= [\frac{3 ^{3 x - 1}}{ln ( 3 )}]_{1}^{4}

限度を計算する:

\frac{177138}{ln ( 3 )}

= \frac{177138}{ln ( 3 )}

グラフ

人気の例

integral from 0 to 1 of (1-x^3)^2x^2

\int_{0}^{1} (1 - x^{3})^{2} x^{2} d x

integral from 4 to x of sqrt(x^2+9)

\int_{4}^{x} x^{2} + 9 d x

integral from pi/4 to pi/2 of csc^2(θ)

\int_{\frac{π}{4}}^{\frac{π}{2}} csc^{2} (θ) d θ

integral from 0 to pi/2 of (xsin(x))

\int_{0}^{\frac{π}{2}} (x sin (x)) d x

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