¿Which is integral of X^X? not to be confused with (a^x) neither with (x^a).?

Answer 1

See the following link for the power series solution:

http://mudandmuck.com/xx.htm

By the way, x^x(1+log(x)) is the derivitive of y=x^x, not the integral.

Answer 2

I agree with the above, I doubt it has a closed form. Just in case you didn't know, that means basically that you'd have to use complicated functions to describe it, or instead use an infinite amount of ink writing out the terms in simpler functions.

Its derivative is simple enough, but the integral seems trickier.

Answer 3

Strictly speaking, there's no closed form. However, if x is known to be positive, then x^x = exp(x ln x). The integral of exp(x ln x) might have a closed form, but I haven't found one.

Answer 4

I don't think it has a closed form. I can't remember one.

I put it in Mathematica and it gave back the same thing I put in.

Answer 5

x^3/3

Answer 6

There is no closed for expression for this anti-derivative. The answer x^x (1+ln x) is the derivative, not the anti-derivative.

Answer 7

According to my TI-92+ which is rather good at these things, there is no solution.

Answer 8

Integration with the help of substitution isn't necessary the following, yet various solutions have used it. workout this crucial with the help of adjusting x with ax + b and dividing with the help of a: ? ln(ax + b) dx = [(ax + b)ln(ax + b) - (ax + b)] / a + C ? ln(ax + b) dx = [(ax + b)ln(ax + b) - ax - b] / a + C ? ln(ax + b) dx = (ax + b)ln(ax + b) / a - x - b / a + C ? ln(ax + b) dx = (ax + b)ln(ax + b) / a - x + C