Question

integrals with trig function in denominator

Answer 1

\[\frac{ dx }{5+4cosx ? }\]

Answer 2

i know you have to let tan =x/2 then sinx = 2t/1+t^2 and cos x = 1-t^2/1+t^2

Answer 3

yes ... you are in right direction

Answer 4

i've solved and ended with \[2\int\limits_{}^{}\frac{ 1+t^2 }{ 5+\frac{ 4-4t^2 }{1+t^2 } }\]

Answer 5

simplify it

Answer 6

if i divide by 1+t^2 then what will happen to the 5?

Answer 7

http://en.wikipedia.org/wiki/Weierstrass_substitution
\[ \int \frac{1}{5 + 4 \cos x} dx = \int \frac{1}{5 + 4 \frac{1-t^2}{1+t^2}} \cdot \frac{2 dt}{1+t^2} = 2 \int \frac{1}{9 + t^2}dt\]
i suppose you can solve after it.