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# Differential Equations/Difficult integral

Question

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

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

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Many thanks for your prompt and helpful response. I hadn't thought of the power series approach, this has given me a lead that may be more computationally efficient than using a numerical solution (e.g. Simpson's Rule). It's great to see there are services out there purely for the purpose of providing help by experts free of charge. Again, I express my thanks for your kind assistance. Regards Peter Thompson

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Differential Equations

Volunteer

#### 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