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受欢迎的微积分 >

integral from 1 to e^3 of (ln^4(x^2))/x

解答

\int_{1}^{e^{3}} \frac{ln ^{4} ( x ^{2} )}{x} d x

解答

\frac{3888}{5}

+1

十进制

777.6

求解步骤

\int_{1}^{e^{3}} \frac{ln ^{4} ( x ^{2} )}{x} d x

化简

\frac{ln ^{4} ( x ^{2} )}{x} : \frac{16 ln ^{4} ( x )}{x}

= \int_{1}^{e^{3}} \frac{16 ln ^{4} ( x )}{x} d x

提出常数:

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

= 16 \cdot \int_{1}^{e^{3}} \frac{ln ^{4} ( x )}{x} d x

使用换元积分法

= 16 \cdot \int_{0}^{3} u^{4} d u

使用幂法则

= 16 [\frac{u ^{5}}{5}]_{0}^{3}

带入上下限计算后得:

\frac{243}{5}

= 16 \cdot \frac{243}{5}

化简

= \frac{3888}{5}

作图

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