Thomas E.

# This was on my first Calc 2 quiz: $2\int_{-3}^{3}e^x^4dx$

I feel that there should be another x in the problem so that u sub works, or something, as it is I believe it is a partial gamma function or something, but I know we should not learn those until much later.

Bobosharif S.

tutor
Hi Thomas, Is the function to be integrated ex^4?

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01/28/18

Arturo O.

Student,

I suggest you restate the integrand in a conventional format.  It is hard to figure out what you mean by  $2\int_{-3}^{3}e^x^4dx$.  That looks like a cut-and-paste from a line of software.
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01/28/18

Thomas E.

No it is not cut/paste. It is \LaTeX. It is one of the languages math is often written in. Some sites support it.
I can write in wolfram if you prefer. It really does not take long to learn any of them. the only odd thing of latex is _ for subscript and ^ for super script.{} is descriptive of previous term.
Integral[Power[e,Power[x,4]],{x,-3,3}]

Or this. The Integral from -3 to 3 of e^(x^4)dx.
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01/29/18

## 2 Answers By Expert Tutors

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David D.

I believe this solution is incorrect!
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07/12/18

Bobosharif S.

tutor
I might agree with you as I see the correct solution.

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07/12/18

David D.

The function e^x^4 has no closed form anti-derivative. That is equivalent to what you said
RE: an error function or an elliptic integral. I didn't see your remarks at the end. My apologies.

They could/should have been made at the end of the first line when the e^t^2 showd up. All the effort with spherical coordinates was merely stretching muscles. The result was obvious even before the first step. So, perhaps algebraically correct  I thought for a moment that you had found an explicit anti-derivative(?) Since it was the first quiz in Calc II, I think the problem is obviously missing an x^3 term which will make it a u-substitution, an easy one. One could integrate by parts a couple times but you never get a "good vdu term to integrate. So why bother with all the fluff?
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07/12/18

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