++$_ wrote:I started with u = sqrt(1+ex).
That got me to (1/2)log(u2-1) (unless I messed up). That should be doable. (Just factor u2-1).
++$_ wrote:If you want to do u2/(u2-1), just add and subtract 1 from the numerator to get 1 + 1/(u2-1). That you should know how to do.
++$_ wrote:You can't integrate 1/(u^2-1)?
Try partial fractions. (Yes, you could also do it with hyperbolic trigonometric functions, but that will just get you the same answer in a more obscure form.)
Fixed, thanks.++$_ wrote:Your last line has an error (it should be u-1/2). It's strongly advised that you now put v = sqrt(u).
One way to integrate log(x) is by parts. One part is log(x). The other part is dx.
Annihilist wrote:I haven't learned how to do integration by parts. I'm leaving it to others in this forum, if anyone can be bothered.
PM 2Ring wrote:d(uv)/dx = vdu/dx + udv/dx
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