integral of (x^{1/2})/2

解答

\int \frac{x ^{\frac{1}{2}}}{2} d x

\frac{1}{3} x^{\frac{3}{2}} + C

求解步骤

\int \frac{x ^{\frac{1}{2}}}{2} d x

提出常数:

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

= \frac{1}{2} \cdot \int x^{\frac{1}{2}} d x

使用幂法则

= \frac{1}{2} \cdot \frac{2}{3} x^{\frac{3}{2}}

化简

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

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

解答补常数

= \frac{1}{3} x^{\frac{3}{2}} + C

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