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 (28)/(4x+xsqrt(x))

解答

\int \frac{28}{4 x + x x} d x

解答

56 (\frac{1}{4} ln x - \frac{1}{4} ln x + 4) + C

求解步骤

\int \frac{28}{4 x + x x} d x

提出常数:

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

= 28 \cdot \int \frac{1}{4 x + x x} d x

使用换元积分法

= 28 \cdot \int \frac{2}{u ( u + 4 )} d u

提出常数:

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

= 28 \cdot 2 \cdot \int \frac{1}{u ( u + 4 )} d u

将

\frac{1}{u ( u + 4 )}

用部份分式展开:

\frac{1}{4 u} - \frac{1}{4 ( u + 4 )}

= 28 \cdot 2 \cdot \int \frac{1}{4 u} - \frac{1}{4 ( u + 4 )} d u

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 28 \cdot 2 (\int \frac{1}{4 u} d u - \int \frac{1}{4 ( u + 4 )} d u)

\int \frac{1}{4 u} d u = \frac{1}{4} ln ∣ u ∣

\int \frac{1}{4 ( u + 4 )} d u = \frac{1}{4} ln ∣ u + 4 ∣

= 28 \cdot 2 (\frac{1}{4} ln ∣ u ∣ - \frac{1}{4} ln ∣ u + 4 ∣)

u = x

代回

= 28 \cdot 2 (\frac{1}{4} ln x - \frac{1}{4} ln x + 4)

化简

= 56 (\frac{1}{4} ln x - \frac{1}{4} ln x + 4)

解答补常数

= 56 (\frac{1}{4} ln x - \frac{1}{4} ln x + 4) + C

作图

流行的例子

limit as x approaches-1/2 of (6x-1)/x

x \to - \frac{1}{2} lim (\frac{6 x - 1}{x})

integral of x^2sqrt(2x-x^2)

\int x^{2} 2 x - x^{2} d x

tangent f(x)=x^3-5x^2,\at x=2

t an g e n t f (x) = x^{3} - 5 x^{2}, at x = 2

(dy)/(dx)=(x^2+xy+y^2)/(x^2)

\frac{d y}{d x} = \frac{x ^{2} + x y + y ^{2}}{x ^{2}}

(\partial)/(\partial z)(-4sqrt(xyz))

\frac{\partial}{\partial z} (- 4 x yz)