integral of 12sqrt(x^5)

解答

\int 12 x^{5} d x

\frac{24}{7} x^{\frac{7}{2}} + C

求解步骤

\int 12 x^{5} d x

提出常数:

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

= 12 \cdot \int x^{5} d x

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

假定

x \geq 0

= 12 \cdot \int x^{\frac{5}{2}} d x

使用幂法则

= 12 \cdot \frac{2}{7} x^{\frac{7}{2}}

化简

12 \cdot \frac{2}{7} x^{\frac{7}{2}} : \frac{24}{7} x^{\frac{7}{2}}

= \frac{24}{7} x^{\frac{7}{2}}

解答补常数

= \frac{24}{7} x^{\frac{7}{2}} + C

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