integral of xg(x^2)

解答

\int xg (x^{2}) d x

\frac{g x ^{4}}{4} + C

求解步骤

\int xg x^{2} d x

提出常数:

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

= g \cdot \int x x^{2} d x

化简

x x^{2} : x^{3}

= g \cdot \int x^{3} d x

使用幂法则

= g \frac{x ^{4}}{4}

分式相乘:

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

= \frac{g x ^{4}}{4}

解答补常数

= \frac{g x ^{4}}{4} + C

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