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^7)/((2-x^8)^2)

解答

\int \frac{x ^{7}}{( 2 - x ^{8} ) ^{2}} d x

解答

\frac{1}{8 ( 2 - x ^{8} )} + C

求解步骤

\int \frac{x ^{7}}{( 2 - x ^{8} ) ^{2}} d x

使用换元积分法

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

提出常数:

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

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

使用幂法则

= - \frac{1}{8} (- \frac{1}{u})

u = 2 - x^{8}

代回

= - \frac{1}{8} (- \frac{1}{2 - x ^{8}})

化简

- \frac{1}{8} (- \frac{1}{2 - x ^{8}}) : \frac{1}{8 ( 2 - x ^{8} )}

= \frac{1}{8 ( 2 - x ^{8} )}

解答补常数

= \frac{1}{8 ( 2 - x ^{8} )} + C

作图

流行的例子

10000y^{''}-81y=0,y(0)=1,y^'(0)=3

10000 y^{^{''}} - 81 y = 0, y (0) = 1, y^{^{'}} (0) = 3

(\partial)/(\partial y)((y^3)/(x^2))

\frac{\partial}{\partial y} (\frac{y ^{3}}{x ^{2}})

y^{^{'}} = - k y^{3}

integral of (1/x+cot(x)-sec(x))

\int (\frac{1}{x} + cot (x) - sec (x)) d x

derivative e^{3*x}*(2*sin(4*x))

d er i v a t i v e e^{3 \cdot x} \cdot (2 \cdot sin (4 \cdot x))