Integration question (1 Viewer)

[Antwan23q]

Just having a bit of trouble from arnoalds 4 unit text book, integration further questions.

I= dx/ x^2.(x-1)^1/2
thanks

 

[haboozin]

Just having a bit of trouble from arnoalds 4 unit text book, integration further questions.

I= dx/ x^2.(x-1)^1/2
thanks

x = u^2 + 1
x' = 2u

so I = 2/(U^2 + 1)^2 du

u = tan@
u' = sec^2 @

I = 2sec^2@/(tan^2@ + 1)^2 d@

tan^2@ + 1 = sec^2@

so I = 2sec^2@/sec^4Q

I = 2cos^2@ d@

I = 1 + cos2@ d@

@ + 1/2sin@cos@ + c

tan^-1 srt(x - 1) + Srt(x - 1)/x + c

if you dont get the last part... draw a right angled triangle

 

[Antwan23q]

ah double integration, i didnt think of using a trig sub after.
thanks