帮忙求这2个不定积分 20
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(1)
let
u=√x
du = dx/[2√x]
dx = 2udu
∫dx/[(1+x).√x]
=2∫du/(1+u^2)
=2arctanu + C
=2arctan√x + C
(2)
let
u=√x
dx = 2udu
∫√{ x / [ 1-x.√x] } dx
=∫√{ u^2/游颤 [ 1-u^3] } .( 2u du)
=2∫ u ^2 . √{ 1/ [ 1-u^3] } du
=-(2/3)∫ d (1-u^3) . /√纯码(1-u^3)
=-(4/3)√神裤败(1-u^3) +C
=-(4/3)√[ 1-x^(3/2) ] +C
let
u=√x
du = dx/[2√x]
dx = 2udu
∫dx/[(1+x).√x]
=2∫du/(1+u^2)
=2arctanu + C
=2arctan√x + C
(2)
let
u=√x
dx = 2udu
∫√{ x / [ 1-x.√x] } dx
=∫√{ u^2/游颤 [ 1-u^3] } .( 2u du)
=2∫ u ^2 . √{ 1/ [ 1-u^3] } du
=-(2/3)∫ d (1-u^3) . /√纯码(1-u^3)
=-(4/3)√神裤败(1-u^3) +C
=-(4/3)√[ 1-x^(3/2) ] +C
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