Question

How about the integration of this:

Answer 1

\[\int\limits\limits_{}^{} \frac{ dx }{ (x-2)\sqrt{x ^{2}-4x+3} }\]

Answer 2

complete the square inside the radical and then let \(u=x-2\) see what happens

Answer 3

oh, ok. wait. I'll try that.

Answer 4

What rule am I supposed to use? Is it the power rule or something? \[x ^{2}-4x+3 = (x-3)(x-1)\] what will happen next?

Answer 5

emm \[x ^{2}-4x+3 =x^2-4x+4-1\]

Answer 6

\[=(x-2)^2-1\]

Answer 7

see ur integral becomes\[\int \frac{\text{d}u}{u\sqrt{u^2-1}}\]

Answer 8

oh. yes, our professor indeed told us that we can do that.
Then the equation with arcsec can now be used! Thank you very much!

Answer 9

k, np :)