integral of (5x)/(3x^{1/3)}

解答

\int \frac{5 x}{3 x ^{\frac{1}{3}}} d x

x^{\frac{5}{3}} + C

求解步骤

\int \frac{5 x}{3 x ^{\frac{1}{3}}} d x

提出常数:

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

= \frac{5}{3} \cdot \int \frac{x}{x ^{\frac{1}{3}}} d x

化简

\frac{x}{x ^{\frac{1}{3}}} : x^{\frac{2}{3}}

= \frac{5}{3} \cdot \int x^{\frac{2}{3}} d x

使用幂法则

= \frac{5}{3} \cdot \frac{3}{5} x^{\frac{5}{3}}

化简

\frac{5}{3} \cdot \frac{3}{5} x^{\frac{5}{3}} : x^{\frac{5}{3}}

= x^{\frac{5}{3}}

解答补常数

= x^{\frac{5}{3}} + C

\int_{- 1}^{1} (3 t - 2) d t

t an g e n t y = 1.1 x + e^{x}, (0, 1)

v o l u m e ab o u t y = 0, y = x^{2}, y = 4 x - x^{2}, [0, 2]

(1 + cos (t)) y^{^{'}} = (1 + e^{- y}) sin (t), y (0) = 0

d er i v a t i v e (x^{2} + 5) (8 - x)