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人気のある微分積分 >

integral from 1 to 2 of x/(sqrt(x-1))

解

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

解

\frac{8}{3}

+1

十進法表記

2.66666 \dots

解答ステップ

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

u置換積分法を適用する

= \int_{0}^{1} 2 (u^{2} + 1) d u

定数を除く:

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

= 2 \cdot \int_{0}^{1} u^{2} + 1 d u

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

= 2 (\int_{0}^{1} u^{2} d u + \int_{0}^{1} 1 d u)

\int_{0}^{1} u^{2} d u = \frac{1}{3}

\int_{0}^{1} 1 d u = 1

= 2 (\frac{1}{3} + 1)

簡素化

2 (\frac{1}{3} + 1) : \frac{8}{3}

= \frac{8}{3}

グラフ

人気の例

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

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

integral from 0 to pi/3 of cos(x)

\int_{0}^{\frac{π}{3}} cos (x) d x

integral from pi/3 to pi of sin(x+pi/3)

\int_{\frac{π}{3}}^{π} sin (x + \frac{π}{3}) d x

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

\int_{0}^{2} \frac{x}{( x ^{2} - 2 x + 2 ) ^{2}} d x

integral from 1 to e of (1+ln(x))/x

\int_{1}^{e} \frac{1 + ln ( x )}{x} d x