Integration by Parts for ∫ xlnx/(x^2-1)^(1/2)dx

[nameVoid]

Homework Statement

I(xlnx/(x^2-1)^(1/2),x)
x=secT ; dx=secTtanTdT
I(secTln(secT)secTtanTdT/tanT,T)
I(sec^2Tln(secT),T)
u=ln(secT) du= secTtanTdT/secT = tanTdT
dv=sec^2Tdt v=tanT
tanTln(secT)- I(tan^2T,T)
tanTln(secT)-I(sec^2-1,T)
tanTln(secT)-tanT+T+C
T=sec^-1x
secT=x
tanT= (x^2-1)^(1/2)
tanTln(secT)-tanT-T= (x^2-1)^(1/2)lnx-(x^2-1)^(1/2)+sec^-1x+C

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Hi nameVoid!

(have an integral: ∫ and a square-root: √ and try using the X² tag just above the Reply box )

Yes, that looks correct, but you could have missed out a lot in the middle if you'd noticed that x/√(x² - 1) is an exact integral, so you can integrate by parts immediately.