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## Main Question or Discussion Point

I tried doing this but could not,why is it so?

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I tried doing this but could not,why is it so?

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Daniel.

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Zurtex

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HallsofIvy

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arildno

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A better question would be:

Why is it simple to integrate f(x)=1?

Why is it simple to integrate f(x)=1?

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arildno

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You won't get any, since an anti-derivative of x^x is inexpressible in terms of elementary functions.abia ubong said:

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Zurtex

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Because as said many times previously in this thread, it can not be integrated in terms of elementary functions.goldi said:

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there must be a solution to it....What it is?

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Zurtex

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There are no special functions defined in general mathematics for the integral.goldi said:

there must be a solution to it....What it is?

If you want a function that is the anti-derivative of x

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matt grime

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i have a question......how can we integrate x*Sec(x)

i have tried this question than any other question ever.....

the point is that it was asked in my 12th class and when i plug it into Integrator i could not even understand the solution...

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arildno

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To integrate x*Sec(x) I would use integration by parts, but in this case the tabular method will work nicely.

[tex]\int x\sec{x}dx[/tex]

[tex]\int udv = uv - \int vdu[/tex]

[tex]u = x[/tex]

[tex]dv = \sec{x}dx[/tex]

That should get you started.

[tex]\int x\sec{x}dx[/tex]

[tex]\int udv = uv - \int vdu[/tex]

[tex]u = x[/tex]

[tex]dv = \sec{x}dx[/tex]

That should get you started.

Last edited:

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I think you meant

[tex] dv=\sec x \ dx [/tex]

I'm not sure though...

Daniel.

[tex] dv=\sec x \ dx [/tex]

I'm not sure though...

Daniel.

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Icebreaker

Has it been done before? Any interesting properties?Zurtex said:If you want a function that is the anti-derivative of x^{x}then just define one and then you can study its properties.

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Pyrrhus

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Look for Liouville's Principle about integration in finite terms.

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that i would have had tried 100 times...after 1 step i am stuck and there is no way out....Jameson said:To integrate x*Sec(x) I would use integration by parts, but in this case the tabular method will work nicely.

[tex]\int x\sec{x}dx[/tex]

[tex]\int udv = uv - \int vdu[/tex]

[tex]u = x[/tex]

[tex]dv = \sec{x}dx[/tex]

That should get you started.

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Well, there's F wheregoldi said:

there must be a solution to it....What it is?

[tex]F(x) = \int_a^x t^t dt [/tex]

and a can be any number greater than or equal to 0. Mathematica isn't able to find that.

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matt grime

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i checked into mathematica,,,it contains some functions of the form polylog but i think this is calculated with the knowledge of Complex Analysis.goldi said:that i would have had tried 100 times...after 1 step i am stuck and there is no way out....

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krab

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You could do it by Taylor expansion:latyph said:I tried doing this but could not,why is it so?

[tex]\int x^x dx=x + \frac{\left( -1 +

2\,\log (x) \right) \,

x^2}{4} +

\frac{\left( 2 -

6\,\log (x) +

9\,{\log (x)}^2 \right)

\,x^3}{54} +

\frac{\left( -3 +

12\,\log (x) -

24\,{\log (x)}^2 +

32\,{\log (x)}^3

\right) \,x^4}{768} +

\frac{\left( 24 -

120\,\log (x) +

300\,{\log (x)}^2 -

500\,{\log (x)}^3 +

625\,{\log (x)}^4

\right) \,x^5}{75000} +

\frac{\left( -5 +

30\,\log (x) -

90\,{\log (x)}^2 +

180\,{\log (x)}^3 -

270\,{\log (x)}^4 +

324\,{\log (x)}^5

\right) \,x^6}{233280}

+ {O(x^7)[/tex]

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shmoe

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