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 (22)/(x^2sqrt(x^2+4))

解答

\int \frac{22}{x ^{2} x ^{2} + 4} d x

解答

- \frac{11 x ^{2} + 4}{2 x} + C

求解步骤

\int \frac{22}{x ^{2} x ^{2} + 4} d x

提出常数:

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

= 22 \cdot \int \frac{1}{x ^{2} x ^{2} + 4} d x

使用三角换元法

= 22 \cdot \int \frac{sec ( u )}{4 tan ^{2} ( u )} d u

提出常数:

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

= 22 \cdot \frac{1}{4} \cdot \int \frac{sec ( u )}{tan ^{2} ( u )} d u

使用三角恒等式改写

= 22 \cdot \frac{1}{4} \cdot \int \frac{cos ( u )}{sin ^{2} ( u )} d u

使用换元积分法

= 22 \cdot \frac{1}{4} \cdot \int \frac{1}{v ^{2}} d v

使用幂法则

= 22 \cdot \frac{1}{4} (- \frac{1}{v})

代回

= 22 \cdot \frac{1}{4} (- \frac{1}{sin ( arctan ( \frac{1}{2} x ) )})

化简

22 \cdot \frac{1}{4} (- \frac{1}{sin ( arctan ( \frac{1}{2} x ) )}) : - \frac{11 x ^{2} + 4}{2 x}

= - \frac{11 x ^{2} + 4}{2 x}

解答补常数

= - \frac{11 x ^{2} + 4}{2 x} + C

作图

流行的例子

derivative (0.09(5^x))/(x^3)

d er i v a t i v e \frac{0.09 ( 5 ^{x} )}{x ^{3}}

derivative (8x)/(7-cot(x))

d er i v a t i v e \frac{8 x}{7 - cot ( x )}

(\partial)/(\partial y)(3ln(x)+ln(y))

\frac{\partial}{\partial y} (3 ln (x) + ln (y))

y^{''}+16y^'=0,y(0)=2,y(0)=-2

y^{^{''}} + 16 y^{^{'}} = 0, y (0) = 2, y (0) = - 2

limit as x approaches 1 of 3x+7

x \to 1 lim (3 x + 7)