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latyph
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I tried doing this but could not,why is it so?
You won't get any, since an anti-derivative of x^x is inexpressible in terms of elementary functions.abia ubong said:i tried doing it ,but always get to a place i can't continue.who can help integrate [(x^x)(1+LOG[X])]^2.All help will be appreciated
Because as said many times previously in this thread, it can not be integrated in terms of elementary functions.goldi said:when i plugged it into the integrator of mathematica it gave it back as same...i don't know why it did not do computation.
There are no special functions defined in general mathematics for the integral.goldi said:i understand that yeah...but even Mathematica couldn't post the solution in terms of complex functions or whatever high level function it ocntains...
there must be a solution to it...What it is?
Zurtex said:If you want a function that is the anti-derivative of xx then just define one and then you can study its properties.
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.
Well, there's F wheregoldi said:i understand that yeah...but even Mathematica couldn't post the solution in terms of complex functions or whatever high level function it ocntains...
there must be a solution to it...What it is?
goldi said:that i would have had tried 100 times...after 1 step i am stuck and there is no way out...
You could do it by Taylor expansion:latyph said:I tried doing this but could not,why is it so?
You are very much right, most people don't understand why we did a course in numerical analysis on my degree program. I think a lot will still have some very naive views on mathematics.shmoe said:I wonder if students aren't done a disservice in first year calculus classes with their sterilized examples and problems. They'll be asked to do hundreds of integration problems, all rigged to work out nicely with the techniques they've just learned. Perhaps it will be mentioned that there are functions whose antiderivatives cannot be written in a "nice" form, but examples will be scarce- [tex]e^{-x^2}[/tex] being the stock one. After seeing such an unnatural ratio of nice examples to possibly one or two 'not-nice' ones, it's no surprise that many walk away believing themselves invincible and any function that itself looks 'nice' will have a 'nice' antiderivative waiting around the corner so they flap their arms around and bash their heads in frustration trying to find it. Makes me wonder if they bother to even consider why numerical techniques are taught at all?
What do you mean "the way it was done", it has no antiderivative other than as definied by a special function. Or are you referring to the integration from -infinity to infinity, that's a different thing than the general antiderivative and can be done in closed form.heman said:[tex]e^{-x^2}[/tex]
This is a nice question ,Our Professor explained it yesterday only and very much amused to find the way it was done.
Yep I really know exactly what you mean. I can remember when I was first learning this stuff and when exp(-x^2) was introduced it was almost like it was this bizarre pathological function just because it didn't have a nice antiderivative.I wonder if students aren't done a disservice in first year calculus classes with their sterilized examples and problems. They'll be asked to do hundreds of integration problems, all rigged to work out nicely with the techniques they've just learned. Perhaps it will be mentioned that there are functions whose antiderivatives cannot be written in a "nice" form, but examples will be scarce- LaTeX graphic is being generated. Reload this page in a moment. being the stock one.
latyph said:I tried doing this but could not,why is it so?
arildno said:There exists, however, no fool-proof technique of constructing anti-derivatives other than by calculating zillions of definite integrals!