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/(sqrt(4x^2+5))

解答

\int \frac{x}{4 x ^{2} + 5} d x

解答

\frac{1}{4} 4 x^{2} + 5 + C

求解步骤

\int \frac{x}{4 x ^{2} + 5} d x

使用换元积分法

= \int \frac{1}{8 u} 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} d u

使用幂法则

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

u = 4 x^{2} + 5

代回

= \frac{1}{8} \cdot 2 (4 x^{2} + 5)^{\frac{1}{2}}

化简

\frac{1}{8} \cdot 2 (4 x^{2} + 5)^{\frac{1}{2}} : \frac{1}{4} 4 x^{2} + 5

= \frac{1}{4} 4 x^{2} + 5

解答补常数

= \frac{1}{4} 4 x^{2} + 5 + C

作图

流行的例子

(\partial)/(\partial x)((rx(K(r,x)-x))/(K(r,x)+ax))

\frac{\partial}{\partial x} (\frac{r x ( K ( r , x ) - x )}{K ( r , x ) + a x})

f (x) = 3 x^{2} + 1

y^'=((4t+y))/(4y-t)

y^{^{'}} = \frac{( 4 t + y )}{4 y - t}

derivative (e^{1/x})/(x^3)

d er i v a t i v e \frac{e ^{\frac{1}{x}}}{x ^{3}}

tangent f(x)=sqrt(x+1),(3,2)

t an g e n t f (x) = x + 1, (3, 2)