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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
Lol.. Oh my..
man, i wish i knew how to do this back in the day. . .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]
I can't see that being much easier because after playing with the algebra it's going to leave many t's with various higher degrees (up to 6th degree if my algebra is correct) and also in a fraction form. After plugging back in tan it's going to have some subs and then reduction formulas for those higher degrees.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]
Yeah I know what you mean, it's just that the integral just looked deceiving simple at first glance.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.Lol.. Oh my..
There has to be an easier way to get this one.