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(1+cos(4x))

解答

\int 1 + cos (4 x) d x

解答

\frac{1}{2} sin (2 x) + C

求解步骤

\int 1 + cos (4 x) d x

使用换元积分法

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

使用三角恒等式改写

= \frac{1}{2} \cdot \int 2 cos^{2} (u) d u

提出常数:

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

= \frac{1}{2} 2 \cdot \int cos^{2} (u) d u

cos^{2} (u) = (cos (u)),

假定

cos (u) \geq 0

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

使用积分常见定则:

\int cos (u) d u = sin (u)

= \frac{1}{2} 2 sin (u)

u = 2 x

代回

= \frac{1}{2} 2 sin (2 x)

化简

\frac{1}{2} 2 sin (2 x) : \frac{1}{2} sin (2 x)

= \frac{1}{2} sin (2 x)

解答补常数

= \frac{1}{2} sin (2 x) + C

作图

流行的例子

derivative of 5sin(x-sin(5x))

\frac{d}{d x} (5 sin (x) - sin (5 x))

inverselaplace (e^{-6s})/(s^2+2s-8)

in v erse l a pl a ce \frac{e ^{- 6 s}}{s ^{2} + 2 s - 8}

integral of (4x+x^2)/(x^2)

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

(\partial)/(\partial x)(xyz-z-sin(x+y))

\frac{\partial}{\partial x} (x yz - z - sin (x + y))

derivative f(x)=ln((x-2)/(x+1))

d er i v a t i v e f (x) = ln (\frac{x - 2}{x + 1})