Warning: Explicit integral could not be found.: What should I do???

Hi, I am doing an trim analysis of an helicopter for forward flight using symbolic math.

Before writing the problem, I obviously tell you this:

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This should be done by using symbolic math only!

(I am using a C81 table for this. I made a fourier-series approximation for that table. And doing some integrations can not be avoided when calculating the Forces and Moments acting on that helicopter.)

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Here is the problem:

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syms t

int(sin(sin(t)),t,0,2*pi)

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After coding this and running this, I always have the result as following:

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*Warning: Explicit integral could not be found.

ans =

int(sin(sin(t)), t = 0..2*pi)*

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I also checked whether the integrand does really exist.

So I plotted the function over x which ranges from 0 to 2pi. And by seeing the graph, nothing made a problem- There are no singularities and it seems to be integrated as u know.

the curve represents the integrand over 0 to 2pi.

Why the symbolic integration does not give me the solution?

Please help me. I fought this for 5 days from night and day.

Actually, the genuine problem is 'much more complex' than this.

This problem is simplified for u to understand clearly what is going on.

[Roger Stafford]

You have unnecessarily restricted yourself to handling your problem with symbolic math only. There are a great many problems in integration and other mathematical problems for which a symbolic solution is simply unknown to mathematicians. In the particular case of int(sin(sin(t)),t,0,2*pi), of course, it is obvious from considerations of symmetry that the answer is 0. (Your plot is inaccurate and should show sin(sin(t)) returning to zero at 2*pi.) However, in general the indefinite integral of sin(sin(t)) is very likely one of a great many integrals which are unknown - at least I can't find it in any of my integral tables. That is undoubtedly why 'int' gave up on the problem and didn't happen to think of using symmetry.

You are very likely going to run into this kind of problem over and over again in your helicopter analysis until you allow yourself to make use of numerical techniques. I would strongly urge you to reconsider the restriction you have placed on your methods.

[Jae Seong Bae]

Ok, I also have thought something about what I posted. My professor and I talked about this and concluded that this symbolic integration might not be necessary for my solution. I am finding another way avoiding the symbolic way. Thank u for your advice. I also realized that the integration formula can not be easily calculated, that is, it should be done by some numerical ways.