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Differential Equations/Difficult integral

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Question
Integral
Integral  
Hi there,

I'm wondering if you can assist with a difficult integral I am trying to solve. It is of the form shown in the accompanying image. I have made a few attempts using substitution and integration by parts. I am an engineer with a reasonable working knowledge of calculus, but this one has defeated me. Can it be solved algebraically, or will I have to use numerical methods?

Many thanks for any assistance you can provide.
Regards
Peter Thompson

Answer
Hello Peter,

That certainly is a tough integral!  I see no way to evaluate it in closed form.
Yes, I believe it will have to be done numerically, or express the integrand as a power
series, then you may be able to express the answer also as a power series.

BTW: You have the variable of integration as "x" as well as the upper limit.  If you wish
to keep "x" as an upper limit, then you should change the variable of integration, say to "t."

Good luck!

A. Mantell

Differential Equations

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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