数学求不定积分∫1⼀1+√(X+2)dx…高手讲下过程哈…谢谢…

数学求不定积分∫1/1+√(X+2)dx… 高手讲下过程哈…谢谢…
2024-11-15 01:43:22
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回答1:

数学求不定积分∫1/1+√(X+2)dx
设u=1+√(X+2),则√(X+2)=u-1
,du=dx/[2√(X+2)]=dx/[2(u-1)]
就是:dx=[2(u-1)]du,
所以,原式=∫2(u-1)du/u=∫2du-∫2du/u
=2u-2Ln|u|+C1
=2[1+√(X+2)]-2Ln|1+√(X+2)|+C1
=2+2√(X+2)-2Ln|1+√(X+2)|+C1
=2√(X+2)-2Ln|1+√(X+2)|+C