∫1/根號x+根號x+1 dx這題求解?
回答 (2)
2017-04-07 8:13 pm
∫1/[√x+√(x+1)] dx這題求解?
Sol
∫1/[√x+√(x+1)] dx
=∫[√(x+1)－√x]/(x+1－x) dx
=∫√(x+1)－√xdx
=∫√(x+1)dx－∫√xdx
=∫(x+1)^(1/2)d(+1)－∫x^(1/2)dx
=2/3(x+1)^(3/2)－x^(2/3)+c
Sol
∫1/[√x+√(x+1)] dx
=∫[√(x+1)－√x]/(x+1－x) dx
=∫√(x+1)－√xdx
=∫√(x+1)dx－∫√xdx
=∫(x+1)^(1/2)d(+1)－∫x^(1/2)dx
=2/3(x+1)^(3/2)－x^(2/3)+c
2017-04-07 4:14 pm
∫[1/根號x+根號x+1] dx
=∫ [x^(-1/2)+x^(1/2)+1] dx
= 2 x^(1/2)+ (2/3) x^(3/2) + x + c
=∫ [x^(-1/2)+x^(1/2)+1] dx
= 2 x^(1/2)+ (2/3) x^(3/2) + x + c
收錄日期: 2021-04-30 22:11:01
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170407050036AA1TfGi