integral from 1 to e of ln(7x)

解答

\int_{1}^{e} ln (7 x) d x

e ln (7 e) - e - ln (7) + 1

十进制

4.34362 \dots

求解步骤

\int_{1}^{e} ln (7 x) d x

使用分布积分法

= [x ln (7 x) - \int 1 d x]_{1}^{e}

\int 1 d x = x

= [x ln (7 x) - x]_{1}^{e}

带入上下限计算后得:

e ln (7 e) - e - ln (7) + 1

= e ln (7 e) - e - ln (7) + 1

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