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Analytical solution to this integral?

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Old   July 28, 2010, 10:00
Default Analytical solution to this integral?
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Anon
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Dear All,

I am currently seeking an analytical model for condensation upon various geometries. I am updating a legacy code, which needs an analytical expression to be entered.

My work on this has led me to the point where I need to evaluate the following integral:
\int\frac{(a+2b\cos{\alpha})\sin{\alpha}}{3(a+b\cos{\alpha})\cos{\alpha}}.d\alpha

Can anyone think of a suitable technique to evaluate this integral analytically? I cannot think of a suitable substitution or transformation.

Many thanks,
T
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Old   July 28, 2010, 10:41
Default solution for the integral
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Ramesh K
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(-log(cos(alpha)b+a) - log(cos(alpha)))/3
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Old   July 28, 2010, 11:21
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That was quick!

Thank you very much ramesh - that worked a treat.
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Old   July 28, 2010, 11:48
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Since a technique was asked in the original question, I would add the following. Since \sin\alpha d \alpha = -d(\cos\alpha) the integral becomes an integral of a rational polynomial. You rewrite integrand as A/(a + b\cos\alpha) + B/\cos\alpha which can then be integrated.
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