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[3]{1-4sin(x)}*cos(x)

解答

\int 3 1 - 4 sin (x) \cdot cos (x) d x

解答

- \frac{3}{16} (1 - 4 sin (x))^{\frac{4}{3}} + C

求解步骤

\int 3 1 - 4 sin (x) cos (x) d x

使用换元积分法

= \int 3 1 - 4 u d u

使用换元积分法

= \int - \frac{3 v}{4} d v

提出常数:

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

= - \frac{1}{4} \cdot \int 3 v d v

使用幂法则

= - \frac{1}{4} \cdot \frac{3}{4} v^{\frac{4}{3}}

代回

= - \frac{1}{4} \cdot \frac{3}{4} (1 - 4 sin (x))^{\frac{4}{3}}

化简

- \frac{1}{4} \cdot \frac{3}{4} (1 - 4 sin (x))^{\frac{4}{3}} : - \frac{3}{16} (1 - 4 sin (x))^{\frac{4}{3}}

= - \frac{3}{16} (1 - 4 sin (x))^{\frac{4}{3}}

解答补常数

= - \frac{3}{16} (1 - 4 sin (x))^{\frac{4}{3}} + C

作图

流行的例子

y^2y^'+y^3=1,y(0)=0

y^{2} y^{^{'}} + y^{3} = 1, y (0) = 0

integral from 2 to infinity of e^{-2x}

\int_{2}^{\infty} e^{- 2 x} d x

derivative f(x)=xcos(x^2)

d er i v a t i v e f (x) = x cos (x^{2})

limit as x approaches 5 of 2x

x \to 5 lim (2 x)

derivative 4sec(x)tan(x)

d er i v a t i v e 4 sec (x) tan (x)