Question

integral dx/x^2-x+2 by trigonometric substitution...

completing the square i got (x-(1/2))^2+7/4

Answer 1

A bit messy, isn't this, Dan?
I agree with your completion of the square.

Now note that you could use the substitution u=x-1/2, ending up with

\[\int\limits_{}^{}\frac{ du }{ u ^{2}+(\frac{ \sqrt{7} }{ 2 })^{2} }\]

Answer 2

You with me so far?

Answer 3

yes

Answer 4

Then, since we're asked to use trig subst., let u=\[u=\frac{ \sqrt{7} }{ 2 }\tan \theta\]

Answer 5

\[u ^{2}=\frac{ 7 }{ 4 }\tan ^{2}\theta;du=\frac{ \sqrt{7} }{ 4 }\sec ^{2}\theta d \theta\]

Answer 6

What would you do next? Have u used this particular trig subst. before?

Answer 7

\[u ^{2}=\frac{ 7 }{ 4 }\tan ^{2}\theta;du=\frac{ \sqrt{7} }{ 2 }\sec ^{2}\theta d \theta\]

Answer 8

yes, i used it, thanks a lot i appreciate it.

Answer 9

My great pleasure. Obviously, once you've integrated with respect to theta, you'll have to work backwards and convert your answer in terms of theta to terms of (x-1/2) and then in terms of x. OK with that?

Answer 10

Just let me know if further questions arise. All the best to you!

Answer 11

yep, ty