integral of-5sqrt(x^4)

解答

\int - 5 x^{4} d x

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

求解步骤

\int - 5 x^{4} d x

提出常数:

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

= - 5 \cdot \int x^{4} d x

x^{4} = x^{2},

假定

x \geq 0

= - 5 \cdot \int x^{2} d x

使用幂法则

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

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

解答补常数

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

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