integral of 10x^{-1/2}

解答

\int 10 x^{- \frac{1}{2}} d x

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

求解步骤

\int 10 x^{- \frac{1}{2}} d x

提出常数:

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

= 10 \cdot \int x^{- \frac{1}{2}} d x

使用幂法则

= 10 \cdot 2 x^{\frac{1}{2}}

化简

= 20 x^{\frac{1}{2}}

解答补常数

= 20 x^{\frac{1}{2}} + C

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