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 x(3x^2+7)^9

解答

\int x (3 x^{2} + 7)^{9} d x

解答

\frac{1}{60} (3 x^{2} + 7)^{10} + C

求解步骤

\int x (3 x^{2} + 7)^{9} d x

使用换元积分法

= \int \frac{u ^{9}}{6} d u

提出常数:

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

= \frac{1}{6} \cdot \int u^{9} d u

使用幂法则

= \frac{1}{6} \cdot \frac{u ^{10}}{10}

u = 3 x^{2} + 7

代回

= \frac{1}{6} \cdot \frac{( 3 x ^{2} + 7 ) ^{10}}{10}

化简

\frac{1}{6} \cdot \frac{( 3 x ^{2} + 7 ) ^{10}}{10} : \frac{1}{60} (3 x^{2} + 7)^{10}

= \frac{1}{60} (3 x^{2} + 7)^{10}

解答补常数

= \frac{1}{60} (3 x^{2} + 7)^{10} + C

作图

流行的例子

integral of 5sin^3(4x)

\int 5 sin^{3} (4 x) d x

in t e g r a l \frac{x ^{1}}{2}

integral of 1/(\sqrt[4]{x^3)+sqrt(x)}

\int \frac{1}{4 x ^{3} + x} d x

integral of (cos(2x))/(sin^4(2x))

\int \frac{cos ( 2 x )}{sin ^{4} ( 2 x )} d x

integral of (6x^3+1/(5x^7)-4)

\int (6 x^{3} + \frac{1}{5 x ^{7}} - 4) d x