integral of (5x-1)^5

解答

\int (5 x - 1)^{5} d x

\frac{1}{30} (5 x - 1)^{6} + C

求解步骤

\int (5 x - 1)^{5} d x

使用换元积分法

= \int \frac{u ^{5}}{5} d u

提出常数:

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

= \frac{1}{5} \cdot \int u^{5} d u

使用幂法则

= \frac{1}{5} \cdot \frac{u ^{6}}{6}

u = 5 x - 1

代回

= \frac{1}{5} \cdot \frac{( 5 x - 1 ) ^{6}}{6}

化简

\frac{1}{5} \cdot \frac{( 5 x - 1 ) ^{6}}{6} : \frac{1}{30} (5 x - 1)^{6}

= \frac{1}{30} (5 x - 1)^{6}

解答补常数

= \frac{1}{30} (5 x - 1)^{6} + C

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