$$\int_1^{10}x^xdx$$ I figured it with a relative error of 1% and I have a response $$≈0.3*10^{10}$$ But I don´t know how to accurately calculate it ...
Calculate the integral $\int_1^{10}x^xdx$
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analysis
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0You cannot find a closed form for $\int x^{x}dx$ (see http://math.stackexchange.com/questions/155/how-can-you-prove-that-a-function-has-no-closed-form-integral/2329#2329 ) – 2010-11-01
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0@Tavares, you don't need to find the antiderivative of a function to accurately calculate its integral, there are many ways to find a convergence series. – 2010-11-01
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0If you just want more accuracy or to check the accuracy of any method, Wolfram alpha can help you out. `http://www.wolframalpha.com/input/?i=int_0^10+x^x` – 2010-11-01
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0@Haengel, I know. My comment was an information in case OP was trying to find a closed form. – 2010-11-01
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1The problem of course with using power series is that they suck at approximating far away from the point of expansion. I would actually just suggest using numerical quadrature if one wants accurate values. – 2010-11-02