zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

integral of (1-3x)^9

解答

\int (1 - 3 x)^{9} d x

解答

- \frac{1}{30} (1 - 3 x)^{10} + C

求解步骤

\int (1 - 3 x)^{9} d x

使用换元积分法

= \int - \frac{u ^{9}}{3} d u

提出常数:

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

= - \frac{1}{3} \cdot \int u^{9} d u

使用幂法则

= - \frac{1}{3} \cdot \frac{u ^{10}}{10}

u = 1 - 3 x

代回

= - \frac{1}{3} \cdot \frac{( 1 - 3 x ) ^{10}}{10}

化简

- \frac{1}{3} \cdot \frac{( 1 - 3 x ) ^{10}}{10} : - \frac{1}{30} (1 - 3 x)^{10}

= - \frac{1}{30} (1 - 3 x)^{10}

解答补常数

= - \frac{1}{30} (1 - 3 x)^{10} + C

作图

流行的例子

integral of (x+ln(1-x))/(x^2)

\int \frac{x + ln ( 1 - x )}{x ^{2}} d x

integral of (3/(x^2)+4-1/(4x^3))

\int (\frac{3}{x ^{2}} + 4 - \frac{1}{4 x ^{3}}) d x

integral of x^1sin(x^2)

\int x^{1} sin (x^{2}) d x

in t e g r a l 4 x^{2}

integral of cos^2((pix)/2)

\int cos^{2} (\frac{π x}{2}) d x