challenge integral

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# challenge integral

Submitted by curious on Tue, 01/29/2008 - 12:45

Forums:

Evaluate integral e^(cos x) dx

Also what is integral (x^2 + 1)^n dx , where n is a constant

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## Re: challenge integral

Evaluate them as indefinite integrals (no limits)

## Re: challenge integral

You can't. Use numerical analysis to obtain an approximation (Try using Taylor's expansion, so you may truncate the series where you want, with a lot of work BTW). An exact solution, in terms of elementary functions, is not known for such integral. For the second one use a recursive formula (or expand out the binomial).

Just only a few classes of functions are integrable in closed form, not that we want.

perucho

## Re: challenge integral

What are the limits of integration? Is this meant as

definite or indefinite integral?

## Re: challenge integral

The second integral can be expanded by binomial theorem and integrated term by term, if n is an integer.

If n is not an integer you will get an infinite series. For the first you can use the power series for e^u and integrate the powers of cosx.