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# Integration- help needed! watch

1. I dont know how to integrate the examples below
a) intg 1/(x sqrt(x-1)) dx
b) intg lnx/(1-x)^2 dx
2. (Original post by a fresh student)
I dont know how to integrate the examples below
a) intg 1/(x sqrt(x-1)) dx
with substitution
sqrt(x-1)=u
b) intg lnx/(1-x)^2 dx
integrating by part
u'=1/(1-x)^2 v=lnx

3. integrating by part
u'=1/(1-x)^2 v=lnx
in that way i get:
lnx/(1-x) - intg 1/((1-x)x) dx

is that correct?
what should i do then?

i thought:
lnx/(1-x) - intg (-1/x + 1/(1-x)) dx = lnx/(1-x) + lnx - ln(x-1) + C

but i am really not sure if its correct :/
4. (Original post by ztibor)

integrating by part
u'=1/(1-x)^2 v=lnx
in that way i get:
lnx/(1-x) - intg 1/((1-x)x) dx

is that correct?
what should i do then?

i thought:
lnx/(1-x) - intg (-1/x + 1/(1-x)) dx = lnx/(1-x) + lnx - ln(x-1) + C

but i am really not sure if its correct :/
5. (Original post by a fresh student)
in that way i get:
lnx/(1-x) - intg 1/((1-x)x) dx

is that correct?
what should i do then?

i thought:
lnx/(1-x) - intg (-1/x + 1/(1-x)) dx = lnx/(1-x) + lnx - ln(x-1) + C

but i am really not sure if its correct :/
Almost correct only a sign

lnx/(1-x)-intg(1/x+1/(1-x))dx

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