integral of (ax)^n

解答

\int (a x)^{n} d x

\frac{a ^{n} x ^{n + 1}}{n + 1} + C

求解步骤

\int (a x)^{n} d x

(a x)^{n} = a^{n} x^{n}

= \int a^{n} x^{n} d x

提出常数:

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

= a^{n} \cdot \int x^{n} d x

使用幂法则

= a^{n} \frac{x ^{n + 1}}{n + 1}

分式相乘:

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

= \frac{a ^{n} x ^{n + 1}}{n + 1}

解答补常数

= \frac{a ^{n} x ^{n + 1}}{n + 1} + C

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