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(x+2)In(x+2)

解

\int 6 (x + 2) I n (x + 2) d x

解

6 I n (4 x + 2 x^{2} + \frac{x ^{3}}{3}) + C

解答ステップ

\int 6 (x + 2) I n (x + 2) d x

定数を除く:

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

= 6 I n \cdot \int (2 + x) (2 + x) d x

簡素化

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

= 6 I n \cdot \int (2 + x)^{2} d x

拡張

(2 + x)^{2} : 4 + 4 x + x^{2}

= 6 I n \cdot \int 4 + 4 x + x^{2} 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

= 6 I n (\int 4 d x + \int 4 x d x + \int x^{2} d x)

\int 4 d x = 4 x

\int 4 x d x = 2 x^{2}

\int x^{2} d x = \frac{x ^{3}}{3}

= 6 I n (4 x + 2 x^{2} + \frac{x ^{3}}{3})

定数を解答に追加する

= 6 I n (4 x + 2 x^{2} + \frac{x ^{3}}{3}) + C

グラフ

人気の例

integral from pi/4 to pi of tan(x)

\int_{\frac{π}{4}}^{π} tan (x) d x

d/(dt)((((sin(t)+(sin(x))^3t))/t)e^t)

\frac{d}{d t} \frac{( sin ( t ) + ( sin ( x ) ) ^{3} t )}{t} e^{t}

sum from n=0 to infinity of (2n)!(x/4)^n

n = 0 \sum \infty (2 n)! (\frac{x}{4})^{n}

integral of x\sqrt[3]{7-6x^2}

\int x 3 7 - 6 x^{2} d x

derivative of e^{1/x}-1

\frac{d}{d x} (e^{\frac{1}{x}} - 1)