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 2 of 5x(x^2+1)

解

\int_{1}^{2} 5 x (x^{2} + 1) d x

解

\frac{105}{4}

+1

十進法表記

26.25

解答ステップ

\int_{1}^{2} 5 x (x^{2} + 1) d x

定数を除く:

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

= 5 \cdot \int_{1}^{2} x (x^{2} + 1) d x

拡張

x (x^{2} + 1) : x^{3} + x

= 5 \cdot \int_{1}^{2} x^{3} + x d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 5 (\int_{1}^{2} x^{3} d x + \int_{1}^{2} x d x)

\int_{1}^{2} x^{3} d x = \frac{15}{4}

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

= 5 (\frac{15}{4} + \frac{3}{2})

簡素化

5 (\frac{15}{4} + \frac{3}{2}) : \frac{105}{4}

= \frac{105}{4}

グラフ

人気の例

integral from 0 to 3 of 10e^{2x}

\int_{0}^{3} 10 e^{2 x} d x

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

\int_{0}^{1} \frac{x - 1}{x ^{2} - 2 x + 3} d x

integral from 4 to t of (12)/(sqrt(x))

\int_{4}^{t} \frac{12}{x} d x

integral from 0 to 1 of e^xx^2

\int_{0}^{1} e^{x} x^{2} d x

integral from 3 to 4 of ln^2(x)

\int_{3}^{4} ln^{2} (x) d x