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受欢迎的微积分 >

integral of (ln(x^{28}))/x

解答

\int \frac{ln ( x ^{28} )}{x} d x

解答

14 ln^{2} (x) + C

求解步骤

\int \frac{ln ( x ^{28} )}{x} d x

使用换元积分法

= \int \frac{ln ( u )}{28 u} d u

提出常数:

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

= \frac{1}{28} \cdot \int \frac{ln ( u )}{u} d u

使用换元积分法

= \frac{1}{28} \cdot \int v d v

使用幂法则

= \frac{1}{28} \cdot \frac{v ^{2}}{2}

代回

= \frac{1}{28} \cdot \frac{ln ^{2} ( x ^{28} )}{2}

化简

\frac{1}{28} \cdot \frac{ln ^{2} ( x ^{28} )}{2} : 14 ln^{2} (x)

= 14 ln^{2} (x)

解答补常数

= 14 ln^{2} (x) + C

作图

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