integral of 1/4 x^2

解答

\int \frac{1}{4} x^{2} d x

\frac{x ^{3}}{12} + C

求解步骤

\int \frac{1}{4} x^{2} d x

提出常数:

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

= \frac{1}{4} \cdot \int x^{2} d x

使用幂法则

= \frac{1}{4} \cdot \frac{x ^{3}}{3}

化简

\frac{1}{4} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{12}

= \frac{x ^{3}}{12}

解答补常数

= \frac{x ^{3}}{12} + C

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