integral of (x^3)^{1/2}

解答

\int (x^{3})^{\frac{1}{2}} d x

\frac{2}{5} x^{\frac{5}{2}} + C

求解步骤

\int (x^{3})^{\frac{1}{2}} d x

(x^{3})^{\frac{1}{2}} = x^{\frac{3}{2}},

假定

x \geq 0

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

使用幂法则

= \frac{2}{5} x^{\frac{5}{2}}

解答补常数

= \frac{2}{5} x^{\frac{5}{2}} + C

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