Question

Integration:

Answer 1

\[\LARGE \int~\frac{dx}{\sqrt{x^2-6x+13}}~dx\]

Answer 2

complete the square for the quadratic inside bottom radical,
then make a trig substitution

Answer 3

So something like? \[\LARGE \int~\frac{dx}{\sqrt{(x-3)^2+4}}~\]
Then sub \(u=x-3\) and go from there>

Answer 4

Yep ! or make the substitution directly in single step :
sub \(\large x-3 = 2\tan u\)

Answer 5

Wait, *-4, not 4.

Answer 6

+4 is right :

9 + 4 = 13

Answer 7

Oh, right, sorry, did that too quickly.

Btw, isn't \(\Large \int~\frac{dx}{\sqrt{1+x^2}}=sinh^{-1}x\) not tan?

Answer 8

that works too^

Answer 9

Alright, thank you rational :)

Answer 10

earlier substitution is for ppl who are familiar wid hyperbolics yet, yw :)

Answer 11

*not