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 (sqrt(x)sec(sqrt(x)))/(3x)

解答

\int \frac{x sec ( x )}{3 x} d x

解答

\frac{2}{3} ln tan (x) + sec (x) + C

求解步骤

\int \frac{x sec ( x )}{3 x} d x

提出常数:

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

= \frac{1}{3} \cdot \int \frac{x sec ( x )}{x} d x

使用三角恒等式改写

= \frac{1}{3} \cdot \int \frac{1}{x cos ( x )} d x

使用换元积分法

= \frac{1}{3} \cdot \int 2 sec (u) d u

提出常数:

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

= \frac{1}{3} \cdot 2 \cdot \int sec (u) d u

使用积分常见定则:

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= \frac{1}{3} \cdot 2 ln ∣ tan (u) + sec (u) ∣

u = x

代回

= \frac{1}{3} \cdot 2 ln tan (x) + sec (x)

化简

\frac{1}{3} \cdot 2 ln tan (x) + sec (x) : \frac{2}{3} ln tan (x) + sec (x)

= \frac{2}{3} ln tan (x) + sec (x)

解答补常数

= \frac{2}{3} ln tan (x) + sec (x) + C

作图

流行的例子

integral from 0 to 6 of f(x)

\int_{0}^{6} f (x) d x

(\partial)/(\partial x)(x^2-2xy+3y^2+2x-2y)

\frac{\partial}{\partial x} (x^{2} - 2 x y + 3 y^{2} + 2 x - 2 y)

derivative of-|x|

\frac{d}{d x} (- ∣ x ∣)

integral of sin(5x)sin(x)

\int sin (5 x) sin (x) d x

integral of e^{t/(RC)}

\int e^{\frac{t}{RC}} d t