乱七八糟翅膀
幼苗
共回答了16个问题采纳率:93.8% 举报
∫(ln3→ln8) √(1 + e^x) dx
令u = √(1 + e^x),x = ln(u² - 1),dx = 2u/(u² - 1)
当x = ln3,u = 2
当x = ln8,u = 3
= ∫(2→3) u * (2u)/(u² - 1) du
= 2∫(2→3) [(u² - 1) + 1]/(u² - 1) du
= 2∫(2→3) [1 + 1/(u² - 1)] du
= 2u |[2→3] + 2*(1/2)ln[(u - 1)/(u + 1)] |[2→3]
= 2(3 - 2) + [ln(2/4) - ln(1/3)]
= 2 + ln[(1/2)/(1/3)]
= 2 + ln(3/2)
= 2 + ln(3) - ln(2)
1年前
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