integration (1 Viewer)

[want2beSMART]

the integral of dx / [sqrt x ( 1+x) ]

 

[FinalFantasy]

the integral of dx / [sqrt x ( 1+x) ]

let u=sqrt(1+x)
u^2=(1+x)
x=u^2-1
dx=2u du
Let I=integral of dx /sqrt x ( 1+x)
I=int. 2u du\u(sqrt(u^2-1)
=2int. du\sqrt(u^2-1)
=2 ln (u+sqrt(u^2-1) )+c
=2ln (sqrt(1+x)+sqrt(x) )+C

 

[want2beSMART]

=2int. du\sqrt(u^2-1)
=2 ln (u+sqrt(u^2-1) )+c
=2ln (sqrt(1+x)+sqrt(x) )+C

i dont get it from here on

how come it is ln (U+sqrt(u^2-1) ) when the U was eliminated in the previous step

 

[ngai]

[sqrt x ( 1+x) ]

is that (sqrt x)(1+x) or sqrt(x(1+x))?

 

[want2beSMART]

is that (sqrt x)(1+x) or sqrt(x(1+x))?

(sqrt x)(1+x)

 

[shafqat]

let u^2 = x
then 2udu = dx
so int. dx/(sqrt x)(1 + x) = int. 2udu/u(1+u^2)
= int. 2du/(1+u^2)
= 2tan-1(u)
= 2tan-1(sqrt x)