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

解答

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

\frac{ln ^{2} ( 2 )}{2} - 2 ln^{2} (2)

十进制

- 0.72067 \dots

求解步骤

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

使用换元积分法

= \int_{- 2 l n (2)}^{l n (2)} u d u

使用幂法则

= [\frac{u ^{2}}{2}]_{- 2 l n (2)}^{l n (2)}

带入上下限计算后得:

\frac{ln ^{2} ( 2 )}{2} - 2 ln^{2} (2)

= \frac{ln ^{2} ( 2 )}{2} - 2 ln^{2} (2)

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