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人気のある微分積分 >

integral from 1 to 2 of 2^{5x}

解

\int_{1}^{2} 2^{5 x} d x

解

\frac{992}{5 ln ( 2 )}

+1

十進法表記

286.23069 \dots

解答ステップ

\int_{1}^{2} 2^{5 x} d x

簡素化

2^{5 x} : 3 2^{x}

= \int_{1}^{2} 3 2^{x} d x

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

= [\frac{3 2 ^{x}}{ln ( 32 )}]_{1}^{2}

簡素化

ln (32) : 5 ln (2)

= [\frac{3 2 ^{x}}{5 ln ( 2 )}]_{1}^{2}

限度を計算する:

\frac{992}{5 ln ( 2 )}

= \frac{992}{5 ln ( 2 )}

グラフ

人気の例

integral from 1 to infinity of 2x^{-2}

\int_{1}^{\infty} 2 x^{- 2} d x

integral from-1 to 3 of |(x+1)(x-2)|

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

integral from 0 to 1 of 25-(t-5)^2

\int_{0}^{1} 25 - (t - 5)^{2} d t

integral from-2 to 2 of x^9

\int_{- 2}^{2} x^{9} d x

integral from 1 to 4 of (2-|x-3|)

\int_{1}^{4} (2 - ∣ x - 3 ∣) d x