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 1/4 e^{sqrt(x-1)}

解答

\int \frac{1}{4} e^{x - 1} d x

解答

\frac{1}{2} (e^{x - 1} x - 1 - e^{x - 1}) + C

求解步骤

\int \frac{1}{4} e^{x - 1} d x

提出常数:

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

= \frac{1}{4} \cdot \int e^{x - 1} d x

使用换元积分法

= \frac{1}{4} \cdot \int e^{u} \cdot 2 u d u

提出常数:

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

= \frac{1}{4} \cdot 2 \cdot \int e^{u} u d u

使用分布积分法

= \frac{1}{4} \cdot 2 (e^{u} u - \int e^{u} d u)

\int e^{u} d u = e^{u}

= \frac{1}{4} \cdot 2 (e^{u} u - e^{u})

u = x - 1

代回

= \frac{1}{4} \cdot 2 (e^{x - 1} x - 1 - e^{x - 1})

化简

\frac{1}{4} \cdot 2 (e^{x - 1} x - 1 - e^{x - 1}) : \frac{1}{2} (e^{x - 1} x - 1 - e^{x - 1})

= \frac{1}{2} (e^{x - 1} x - 1 - e^{x - 1})

解答补常数

= \frac{1}{2} (e^{x - 1} x - 1 - e^{x - 1}) + C

作图

流行的例子

derivative 3e^x+4/(\sqrt[3]{x)}

d er i v a t i v e 3 e^{x} + \frac{4}{3 x}

derivative of 1/(10-x)

\frac{d}{d x} (\frac{1}{10 - x})

integral of (ye^{xy})

\int (y e^{x y}) d x

integral of 1.8^{0.045x}

\int 1. 8^{0.045 x} d x

integral of ((x^2))/((x+3)^3)

\int \frac{( x ^{2} )}{( x + 3 ) ^{3}} d x