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## Main Question or Discussion Point

The function is continuous so the integral exists, but how do you find it :)?

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The function is continuous so the integral exists, but how do you find it :)?

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rock.freak667

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Let [itex]x=e^t \Rightarrow \frac{dx}{dt}=e^t=x[/itex]

[tex]\int sin(e^t) dt \equiv \int \frac{sinx}{x}dx[/tex]

and that doesn't exist in terms of elementary functions

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Hey!

Why can't you use the method of intergation by Parts for [tex]\int sin(e^x) dt[/tex]?

We CAN think that this integral is in the form [tex]\int f(x) g(x) dx[/tex], right?

I think it can be done using the formula of integration by parts, [tex]\int uv' = uv - \int v u'[/tex]. This might be done that way imo.

Why can't you use the method of intergation by Parts for [tex]\int sin(e^x) dt[/tex]?

We CAN think that this integral is in the form [tex]\int f(x) g(x) dx[/tex], right?

I think it can be done using the formula of integration by parts, [tex]\int uv' = uv - \int v u'[/tex]. This might be done that way imo.

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Go ahead and try. Be prepared to be frustrated, however because ...Hey!

Why can't you use the method of intergation by Parts for [tex]\int sin(e^x) dt[/tex]?

This latter integral is encountered in math and science quite frequently, so frequently that it has been given a name -- the sine integral. For more info, see[tex]\int sin(e^t) dt \equiv \int \frac{sinx}{x}dx[/tex]

and that doesn't exist in terms of elementary functions

http://planetmath.org/encyclopedia/SinusIntegralis.html" [Broken]

http://mathworld.wolfram.com/SineIntegral.html" [Broken]

http://en.wikipedia.org/wiki/Sine_integral" [Broken]

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HallsofIvy

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Why would you think so? If it were eHey!

Why can't you use the method of intergation by Parts for [tex]\int sin(e^x) dt[/tex]?

We CAN think that this integral is in the form [tex]\int f(x) g(x) dx[/tex], right?

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It's just weird.. because my math teacher says that if the funciton is continuous the integral exists, but that must only be with a definite integral then.

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What

The integral exists, but we can't express it in terms of elementary functions.... that doesn't exist in terms of elementary functions

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