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 of 6/(xsqrt(x^2+1))

解

\int \frac{6}{x x ^{2} + 1} d x

解

- 6 (\frac{1}{2} ln x^{2} + 1 + 1 - \frac{1}{2} ln x^{2} + 1 - 1) + C

解答ステップ

\int \frac{6}{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

= 6 \cdot \int \frac{1}{x x ^{2} + 1} d x

u置換積分法を適用する

= 6 \cdot \int \frac{1}{u ^{2} - 1} d u

因数

u^{2} - 1 : - (- u^{2} + 1)

= 6 \cdot \int \frac{1}{- ( - u ^{2} + 1 )} d u

定数を除く:

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

= 6 (- \int \frac{1}{- u ^{2} + 1} d u)

共通積分を使用する:

\int \frac{1}{- u ^{2} + 1} d u = \frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2}

= 6 (- (\frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2}))

代用を戻す

u = x^{2} + 1

= 6 (- (\frac{ln x ^{2} + 1 + 1}{2} - \frac{ln x ^{2} + 1 - 1}{2}))

簡素化

6 (- (\frac{ln x ^{2} + 1 + 1}{2} - \frac{ln x ^{2} + 1 - 1}{2})) : - 6 (\frac{1}{2} ln x^{2} + 1 + 1 - \frac{1}{2} ln x^{2} + 1 - 1)

= - 6 (\frac{1}{2} ln x^{2} + 1 + 1 - \frac{1}{2} ln x^{2} + 1 - 1)

定数を解答に追加する

= - 6 (\frac{1}{2} ln x^{2} + 1 + 1 - \frac{1}{2} ln x^{2} + 1 - 1) + C

グラフ

人気の例

integral of (x+1)e^{9x^2+18x}

\int (x + 1) e^{9 x^{2} + 18 x} d x

(d^2y)/(dx^2)-4(dy)/(dx)+13y=8sin(3x),y(0)=1,y^'(0)=2

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 13 y = 8 sin (3 x), y (0) = 1, y^{^{'}} (0) = 2

limit as x approaches 1 of (9x^2)+30x+25

x \to 1 lim ((9 x^{2}) + 30 x + 25)

laplacetransform 4y

l a pl a ce t r an s f or m 4 y

integral of x^{25}sin(x^{26})

\int x^{25} sin (x^{26}) d x