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 (-15)/(x^2sqrt(x^2+4))

解答

\int \frac{- 15}{x ^{2} x ^{2} + 4} d x

解答

\frac{15 4 + x ^{2}}{4 x} + C

求解步骤

\int \frac{- 15}{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

= - 15 \cdot \int \frac{1}{x ^{2} x ^{2} + 4} d x

使用三角换元法

= - 15 \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

= - 15 \cdot \frac{1}{4} \cdot \int \frac{sec ( u )}{tan ^{2} ( u )} d u

使用三角恒等式改写

= - 15 \cdot \frac{1}{4} \cdot \int \frac{cos ( u )}{sin ^{2} ( u )} d u

使用换元积分法

= - 15 \cdot \frac{1}{4} \cdot \int \frac{1}{v ^{2}} d v

使用幂法则

= - 15 \cdot \frac{1}{4} (- \frac{1}{v})

代回

= - 15 \cdot \frac{1}{4} (- \frac{1}{sin ( arctan ( \frac{1}{2} x ) )})

化简

- 15 \cdot \frac{1}{4} (- \frac{1}{sin ( arctan ( \frac{1}{2} x ) )}) : \frac{15 4 + x ^{2}}{4 x}

= \frac{15 4 + x ^{2}}{4 x}

解答补常数

= \frac{15 4 + x ^{2}}{4 x} + C

作图

流行的例子

integral of 3(x^4)/(e^{x^5)}

\int 3 \frac{x ^{4}}{e ^{x^{5}}} d x

integral from 0 to pi/4 of 1

\int_{0}^{\frac{π}{4}} 1

derivative 9x+1-x^2

d er i v a t i v e 9 x + 1 - x^{2}

limit as x approaches 1 of (x^2-3x)/(x-1)

x \to 1 lim (\frac{x ^{2} - 3 x}{x - 1})

integral of (e^{2y})/(sqrt(e^y-1))

\int \frac{e ^{2 y}}{e ^{y} - 1} d y