Thread: integrate!

Hi I have problems integrating two questions, how do I integrate sqrt(x^2-4) / x? And (4lnx) / (x(1+(lnx)^2)? Thank you very much!!

For the second problem, first use t= ln(x), then use z = 1+ t^2. Hope this helps!

Hello, Tutu!

It should be obvious that a Trig Substitution is called for.


Let

Substitute: .

. . . . . . . .

Now back-substitute.

Originally Posted by coolge

For the second problem, first use t= ln(x), then use z = 1+ t^2. Hope this helps!

Which is, of course, the same as the single substitution z= 1+ (ln(x))^2.

Originally Posted by HallsofIvy

Which is, of course, the same as the single substitution z= 1+ (ln(x))^2.

My two cents. I prefer to use two separate substitutions rather than one more complicated one. I can keep better track that way. Or maybe I'm just a coward.

-Dan