ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral from 1 to 3 of 3(2^{x+1})

解

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

解

\frac{36}{ln ( 2 )}

+1

十進法表記

51.93702 \dots

解答ステップ

\int_{1}^{3} 3 \cdot 2^{x + 1} d x

定数を除く:

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

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

2^{x + 1} = 2^{1} \cdot 2^{x}

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

定数を除く:

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

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

簡素化

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

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

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

簡素化

= 6 [\frac{2 ^{x}}{ln ( 2 )}]_{1}^{3}

限度を計算する:

\frac{6}{ln ( 2 )}

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

簡素化

= \frac{36}{ln ( 2 )}

グラフ

人気の例

(dy)/(dx)=x^6y^{-3},y(0)=4

\frac{d y}{d x} = x^{6} y^{- 3}, y (0) = 4

f(x)=x^{log_{10}(x)}

f (x) = x^{l o g_{10} (x)}

integral of x/(ax+b)

\int \frac{x}{a x + b} d x

integral from-3 to-5 of (-5)^{-3}

\int_{- 3}^{- 5} (- 5)^{- 3} d x

derivative of-(y^2/((x-y)^2))

\frac{d}{d x} (- \frac{y ^{2}}{( x - y ) ^{2}})