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 from 0 to 1 of (2x)/((x^2+3)^3)

解答

\int_{0}^{1} \frac{2 x}{( x ^{2} + 3 ) ^{3}} d x

解答

\frac{7}{288}

+1

十进制

0.02430 \dots

求解步骤

\int_{0}^{1} \frac{2 x}{( x ^{2} + 3 ) ^{3}} d x

提出常数:

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

= 2 \cdot \int_{0}^{1} \frac{x}{( x ^{2} + 3 ) ^{3}} d x

使用换元积分法

= 2 \cdot \int_{3}^{4} \frac{1}{2 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}{2} \cdot \int_{3}^{4} \frac{1}{u ^{3}} d u

使用幂法则

= 2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{3}^{4}

化简

2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{3}^{4} : [- \frac{1}{2 u ^{2}}]_{3}^{4}

= [- \frac{1}{2 u ^{2}}]_{3}^{4}

带入上下限计算后得:

\frac{7}{288}

= \frac{7}{288}

作图

流行的例子

limit as x approaches infinity of ((e^{x^4-x^2}))/2

x \to \infty lim \frac{( e ^{x^{4} - x^{2}} )}{2}

derivative f(x)=xsqrt(1+x^2)

d er i v a t i v e f (x) = x 1 + x^{2}

integral of (e^{-2x})/(1+e^{-x)}

\int \frac{e ^{- 2 x}}{1 + e ^{- x}} d x

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

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

sum from n=0 to infinity of 1/(n^2+3)

n = 0 \sum \infty \frac{1}{n ^{2} + 3}