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 2x(x^2+5)^8

解答

\int 2 x (x^{2} + 5)^{8} d x

解答

\frac{1}{9} (x^{2} + 5)^{9} + C

求解步骤

\int 2 x (x^{2} + 5)^{8} d x

提出常数:

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

= 2 \cdot \int x (x^{2} + 5)^{8} d x

使用换元积分法

= 2 \cdot \int \frac{u ^{8}}{2} d u

提出常数:

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

= 2 \cdot \frac{1}{2} \cdot \int u^{8} d u

使用幂法则

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{9}}{9}

u = x^{2} + 5

代回

= 2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{9}}{9}

化简

2 \cdot \frac{1}{2} \cdot \frac{( x ^{2} + 5 ) ^{9}}{9} : \frac{1}{9} (x^{2} + 5)^{9}

= \frac{1}{9} (x^{2} + 5)^{9}

解答补常数

= \frac{1}{9} (x^{2} + 5)^{9} + C

作图

流行的例子

integral of 11x

\int 11 x d x

derivative of 2^x-1

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

(dy)/(dt)+e^ty=-2e^t

\frac{d y}{d t} + e^{t} y = - 2 e^{t}

d/(dq)(-0.1q^2+1.2q+46.4)

\frac{d}{d q} (- 0.1 q^{2} + 1.2 q + 46.4)

sum from n=1 to infinity of (9/8)^n

n = 1 \sum \infty (\frac{9}{8})^{n}