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 2x^2cos(x^3)

解答

\int 2 x^{2} cos (x^{3}) d x

解答

\frac{2}{3} sin (x^{3}) + C

求解步骤

\int 2 x^{2} cos (x^{3}) d x

提出常数:

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

= 2 \cdot \int x^{2} cos (x^{3}) d x

使用换元积分法

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

提出常数:

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

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

使用积分常见定则:

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

= 2 \cdot \frac{1}{3} sin (u)

u = x^{3}

代回

= 2 \cdot \frac{1}{3} sin (x^{3})

化简

2 \cdot \frac{1}{3} sin (x^{3}) : \frac{2}{3} sin (x^{3})

= \frac{2}{3} sin (x^{3})

解答补常数

= \frac{2}{3} sin (x^{3}) + C

作图

流行的例子

derivative of 2xsqrt(y-1)

\frac{d}{d x} (2 x y - 1)

limit as x approaches 3 of 2x-8

x \to 3 lim (2 x - 8)

integral of sqrt(9t^4+4t^2)

\int 9 t^{4} + 4 t^{2} d t

(\partial)/(\partial x)(x+y-320)

\frac{\partial}{\partial x} (x + y - 320)

derivative of e^{x^2}y=x

\frac{d}{d x} (e^{x^{2}} y) = x