integral of (3sqrt(x))/(-2)

解答

\int \frac{3 x}{- 2} d x

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

求解步骤

\int \frac{3 x}{- 2} d x

提出常数:

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

= \frac{3}{- 2} \cdot \int x d x

化简

= (- \frac{3}{2}) \cdot \int x d x

使用幂法则

= (- \frac{3}{2}) \frac{2}{3} x^{\frac{3}{2}}

化简

(- \frac{3}{2}) \frac{2}{3} x^{\frac{3}{2}} : - x^{\frac{3}{2}}

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

解答补常数

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

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