- #1
- 1
- 0
Homework Statement
∫ 1 /( sin x + sec x) dx
Homework Equations
The Attempt at a Solution
∫ cos x / ( sin x + cos x ) style question
Tried ∫ cos x / (sin x . cos x + 1) dx
and uses sin 2x
tried substitutions
nothing seem to work
Highway said:
Dickfore said:You can always reduce it to an integral with rational algebraic expressions with the substitution:
[tex]
t \equiv \tan \left( \frac{x}{2} \right)
[/tex]
[tex]
\sin x = \frac{2 t}{1 + t^2}, \ \cos x = \frac{1 - t^2}{1 + t^2}, \ dx = \frac{2 \, dt}{1 + t^2}
[/tex]
Dickfore said:You can always reduce it to an integral with rational algebraic expressions with the substitution:
[tex]
t \equiv \tan \left( \frac{x}{2} \right)
[/tex]
[tex]
\sin x = \frac{2 t}{1 + t^2}, \ \cos x = \frac{1 - t^2}{1 + t^2}, \ dx = \frac{2 \, dt}{1 + t^2}
[/tex]
Dickfore said:No one said the result should have a simple form. Given the integrand, no other simpler substitution seems possible. But, you need to do the partial fraction decomposition yourself, or at least bring the integral in a rational algebraic form if you want further help.
There is.DrummingAtom said:Lol.. Oh my..
There has to be an easier way to get this one.