求下列定积分 ∫(上¾ 下0) 1⼀(x+1)√(x²+1)dx

2025-03-05 03:07:18
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回答1:

∫(0,3/4) 1/(x+1)√(x²+1)dx 令:x=tant
=∫(0,3/4) tantsect/(tant+1)sectdt
= 3/4 - ∫(0,3/4) 1/(tant+1)sectdt
=3/4 - 1/2∫(0,3/4) [(cost+sint)+(sint-cost)]/(sint+cost)dt