integral from 6 to 36 of 1/(x(ln(x))^6)

解答

\int_{6}^{36} \frac{1}{x ( ln ( x ) ) ^{6}} d x

\frac{31}{160 ln ^{5} ( 6 )}

十进制

0.01049 \dots

求解步骤

\int_{6}^{36} \frac{1}{x ( ln ( x ) ) ^{6}} d x

使用换元积分法

= \int_{l n (6)}^{2 l n (6)} \frac{1}{u ^{6}} d u

使用幂法则

= [- \frac{1}{5 u ^{5}}]_{l n (6)}^{2 l n (6)}

带入上下限计算后得:

\frac{31}{160 ln ^{5} ( 6 )}

= \frac{31}{160 ln ^{5} ( 6 )}

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