Integral t = tan(x/2) substitution

by G01
Tags: integral, substitution, tanx or 2
 PF Patron HW Helper P: 2,688 $$\int \frac{dx}{5 - 3\sin x + 4 cos x}$$ I know I have to use t = tan(x/2) substitution, and after i do that and symplify I get: $$\int \frac{dt}{2t^2 - 3t + 1}$$ I dont know where to go from here. If anyone can see where to go, please help. Also, if there is an easier way to do this, please tell me!! Thanks.
 PF Patron Sci Advisor Emeritus P: 16,094 One of your integral techniques is specifically for integrating fractions with polynomials in the denominator...
 PF Patron HW Helper P: 2,688 Sry that second integral had a 1 in the denominator instead of a 2. And that six is supposed to be a 3. I guess your saying partial fractions will work. I'll try it
PF Patron
HW Helper
P: 2,688

Integral t = tan(x/2) substitution

$$| \ln \frac{\tan(x/2) - 1}{2\tan(x/2) - 1)^2} + C$$
 P: 167 Hmm, I think there is something wrong with your expression $$\int \frac{dt}{2t^2 - 3t + 1}$$ I tried doing the substitution myself and the expression in the denominator was a "perfect square". Maybe you can show us how you did the substitution, or you can try checking your work again...