∫根号下(1+x^1/2)dx

来源：学生作业帮助网编辑：作业帮时间：2024/05/13 09:52:10

∫根号下(1+x^1/2)dx
∫根号下(1+x^1/2)dx

∫根号下(1+x^1/2)dx

令a=√(1+√x)
x=(a²-1)²=a^4-2a²+1
dx=(4a³-4a)da
所以原式=∫a(4a³-4a)da
=∫(4a^4-4a²)da
=4a^5/5-4a³/3+C
=4(1+√x)²√(1+√x)/5-4(1+√x)√(1+√x)/3+C

∫√(1+√x) dx
let
√x = (tany)^2
[1/(2√x)]dx = 2tany. (secy)^2 dy
dx = 4(tany)^3. (secy)^2 dy
∫√(1+√x) dx
=4∫(tany)^3. (secy)^3 dy
=4∫ (tany)^2 (secy)^2 dsecy
=4∫ [(secy)^...

全部展开

∫√(1+√x) dx
let
√x = (tany)^2
[1/(2√x)]dx = 2tany. (secy)^2 dy
dx = 4(tany)^3. (secy)^2 dy
∫√(1+√x) dx
=4∫(tany)^3. (secy)^3 dy
=4∫ (tany)^2 (secy)^2 dsecy
=4∫ [(secy)^4 - (secy)^2] dsecy
= 4[ (secy)^5/5 - (secy)^3/3 ]+ C
= 4[ (√(1+√x))^5/5 - (√(1+√x))^3/3 ]+ C
where
√x = (tany)^2
x^(1/4) = tany
secy = √(1+√x)

收起

∫x-根号下x dx ∫lx-2l dx ∫1/根号下（4-x^2) dx ∫e^(-x) dx ∫2/根号下x dx ∫(1/x^2)sin(1/x) dx ∫dx/1+根号下x ∫ (x+1)/(根号下1-x^2)dx 高数 ∫ dx/(2+x)根号下1+x ∫根号下(1+x^1/2)dx 求不定积分∫dx/根号下(1-2x^2), 求积分 ∫根号下（x^2+1）dx ∫（arcsinx）/根号下1-x^2 dx ∫(ln2,0)根号下(1-e^(-2x) )dx ∫(根号下arctanx/1+x^2)dx ；∫((arcsinx)^2/根号下1-x^2)dx；∫e^xcos(e^x+1)dx 不定积分 dx/[(1+x)*根号下x] 不定积分 dx/[(1+x)*根号下x] 求不定积分x ∫（1-x^2）/x根号下x dx∫（1-x^2）/x*根号下x dx 不定积分dx/根号下1+x-x^2= 积分dx/x*根号下（x^2-1）积分号x*根号下(1-x^2)dx 求不定积分 dx/(x^4 *根号下1+x^2) 求不定积分x根号下1+x^2dx