integral of (2000)/(sqrt(300x))

解答

\int \frac{2000}{300 x} d x

\frac{400}{3} x + C

求解步骤

\int \frac{2000}{300 x} d x

提出常数:

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

= 2000 \cdot \int \frac{1}{300 x} d x

使用分布积分法

= 2000 (\frac{1}{10 3} x - \int - \frac{1}{20 3 x ^{\frac{1}{2}}} d x)

\int - \frac{1}{20 3 x ^{\frac{1}{2}}} d x = - \frac{1}{10 3} x

= 2000 (\frac{1}{10 3} x - (- \frac{1}{10 3} x))

化简

2000 (\frac{1}{10 3} x - (- \frac{1}{10 3} x)) : \frac{400}{3} x

= \frac{400}{3} x

解答补常数

= \frac{400}{3} x + C

\frac{d}{d x} (- \frac{3}{2} x^{3} - 2 x^{5} - 5 x^{2})

\frac{d}{d x} (1 + 3 x)

\frac{d y}{d x} = \frac{1}{4 y ^{3}}

\frac{d}{d x} (\frac{x ^{2} - 49}{x - 7})

\int 2 + 2 sin (θ) d θ