integral of 3/(\sqrt[5]{x^2)}

解答

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

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

求解步骤

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

提出常数:

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

= 3 \cdot \int \frac{1}{5 x ^{2}} d x

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

假定

x \geq 0

= 3 \cdot \int \frac{1}{x ^{\frac{2}{5}}} d x

使用幂法则

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

化简

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

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

解答补常数

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

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