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 4 of 1/(2sqrt(x)+3)

解

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

解

\frac{- 3 ln ( 7 ) + 3 ln ( 5 )}{2} + 1

+1

十進法表記

0.49529 \dots

解答ステップ

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

u置換積分法を適用する

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

定数を除く:

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

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

u置換積分法を適用する

= 2 \cdot \int_{5}^{7} \frac{v - 3}{4 v} d v

定数を除く:

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

= 2 \cdot \frac{1}{4} \cdot \int_{5}^{7} \frac{v - 3}{v} d v

拡張

\frac{v - 3}{v} : 1 - \frac{3}{v}

= 2 \cdot \frac{1}{4} \cdot \int_{5}^{7} 1 - \frac{3}{v} d v

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 \cdot \frac{1}{4} (\int_{5}^{7} 1 d v - \int_{5}^{7} \frac{3}{v} d v)

\int_{5}^{7} 1 d v = 2

\int_{5}^{7} \frac{3}{v} d v = 3 (ln (7) - ln (5))

= 2 \cdot \frac{1}{4} (2 - 3 (ln (7) - ln (5)))

簡素化

2 \cdot \frac{1}{4} (2 - 3 (ln (7) - ln (5))) : \frac{- 3 ln ( 7 ) + 3 ln ( 5 )}{2} + 1

= \frac{- 3 ln ( 7 ) + 3 ln ( 5 )}{2} + 1

グラフ

人気の例

integral from 0 to pi of 2sin^2(4x)

\int_{0}^{π} 2 sin^{2} (4 x) d x

integral from 0 to pi/2 of 1/(3+5cos(x))

\int_{0}^{\frac{π}{2}} \frac{1}{3 + 5 cos ( x )} d x

integral from 4 to 5 of (x-4)-(x-4)^3

\int_{4}^{5} (x - 4) - (x - 4)^{3} d x

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

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

integral from-1 to 2 of 4x^3+8x+3

\int_{- 1}^{2} 4 x^{3} + 8 x + 3 d x