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/(1+49x^4)

解答

\int \frac{x}{1 + 49 x ^{4}} d x

解答

\frac{1}{14} arctan (7 x^{2}) + C

求解步骤

\int \frac{x}{1 + 49 x ^{4}} d x

使用换元积分法

= \int \frac{1}{2 ( 1 + 49 u ^{2} )} d u

提出常数:

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

= \frac{1}{2} \cdot \int \frac{1}{1 + 49 u ^{2}} d u

使用换元积分法

= \frac{1}{2} \cdot \int \frac{1}{7 ( 1 + v ^{2} )} d v

提出常数:

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

= \frac{1}{2} \cdot \frac{1}{7} \cdot \int \frac{1}{1 + v ^{2}} d v

使用积分常见定则:

\int \frac{1}{1 + v ^{2}} d v = arctan (v)

= \frac{1}{2} \cdot \frac{1}{7} arctan (v)

代回

= \frac{1}{2} \cdot \frac{1}{7} arctan (7 x^{2})

化简

\frac{1}{2} \cdot \frac{1}{7} arctan (7 x^{2}) : \frac{1}{14} arctan (7 x^{2})

= \frac{1}{14} arctan (7 x^{2})

解答补常数

= \frac{1}{14} arctan (7 x^{2}) + C

作图

流行的例子

integral of ((5-4x))/(sqrt(12x-4x^2-8))

\int \frac{( 5 - 4 x )}{12 x - 4 x ^{2} - 8} d x

integral of 6x^2+6x

\int 6 x^{2} + 6 x d x

integral of 1/(x+2sqrt(x))

\int \frac{1}{x + 2 x} d x

integral of 4e^{4x}sin(4x)

\int 4 e^{4 x} sin (4 x) d x

integral of (2sin(x))/(e^x)

\int \frac{2 sin ( x )}{e ^{x}} d x