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-2 to 2 of (10)/(x^2-4x-21)

解

\int_{- 2}^{2} \frac{10}{x ^{2} - 4 x - 21} d x

解

- 2 ln (3)

+1

十進法表記

- 2.19722 \dots

解答ステップ

\int_{- 2}^{2} \frac{10}{x ^{2} - 4 x - 21} d x

定数を除く:

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

= 10 \cdot \int_{- 2}^{2} \frac{1}{x ^{2} - 4 x - 21} d x

以下の部分分数を得る:

\frac{1}{x ^{2} - 4 x - 21} : - \frac{1}{10 ( x + 3 )} + \frac{1}{10 ( x - 7 )}

= 10 \cdot \int_{- 2}^{2} - \frac{1}{10 ( x + 3 )} + \frac{1}{10 ( x - 7 )} 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

= 10 (- \int_{- 2}^{2} \frac{1}{10 ( x + 3 )} d x + \int_{- 2}^{2} \frac{1}{10 ( x - 7 )} d x)

\int_{- 2}^{2} \frac{1}{10 ( x + 3 )} d x = \frac{1}{10} ln (5)

\int_{- 2}^{2} \frac{1}{10 ( x - 7 )} d x = \frac{1}{10} (ln (5) - 2 ln (3))

= 10 (- \frac{1}{10} ln (5) + \frac{1}{10} (ln (5) - 2 ln (3)))

簡素化

10 (- \frac{1}{10} ln (5) + \frac{1}{10} (ln (5) - 2 ln (3))) : - 2 ln (3)

= - 2 ln (3)

グラフ

人気の例

integral of (3sec(x)tan(x)-5csc^2(x))

\int (3 sec (x) tan (x) - 5 csc^{2} (x)) d x

derivative of acos(wx)

\frac{d}{d x} (a cos (w x))

integral of 4^u

\int 4^{u} d u

sum from n=1 to infinity of 2/(2^n)

n = 1 \sum \infty \frac{2}{2 ^{n}}

integral of x(sin^2(x))

\int x (sin^{2} (x)) d x