Question

How do you find the integral of 4/(x^2+2x+5) using trig substitution?

Answer 1

start by completing the squares for the denominator

Answer 2

okay; that makes sense now. thanks!

Answer 3

anymore questions?

Answer 4

no :) I just didn't know how to start the problem.

Answer 5

\[4 \int\limits \frac{1}{x^2+2 x+5} \, dx\]
CTS
\[4 \int\limits \frac{1}{4+(x+1)^2} \, dx\]
Factor 4
\[ \int\limits \frac{1}{ \left(1+\frac{u^2}{4}\right)} \, du\]
Trig substitution here

Answer 6

ok, thanks. so it would be 2arctan((x+1)/2) + c

Answer 7

Yes.