integral of 1/(sqrt(x\sqrt{x))}

解答

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

4 4 x + C

求解步骤

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

化简

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

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

x^{\frac{3}{2}} = x^{\frac{3}{4}},

假定

x \geq 0

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

使用幂法则

= 4 x^{\frac{1}{4}}

使用根式运算法则:

a^{\frac{1}{n}} = n a

= 4 4 x

解答补常数

= 4 4 x + C

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