Question

Question #6a649

Answer 1

See below.

Explanation:

This is an integral that cannot be obtained in closed form. In those cases you can try to integrate the series representation to obtain an answer.

Taking as an example

`int x^x dx` which is also an integral not obtainable in closed form,
developping in series

`(1+x)^(1+x) = sum_(k=0)^oo((Pi_(j=1)^k(x-j+2))/(k!))x^k` or

`(1+x)^(1+x) = 1 + x (1 + x) + 1/2 x^3 (1 + x) + 1/6 (x-1) x^4 (1 + x)+cdots`

Convergent for `-1le x le 1`

Now, with `0 le x le 2` you can approximate the integral obtaining

`intx^xdx approx sum_(k=0)^nint((Pi_(j=1)^k(x-j+1))/(k!))(x-1)^kdx`