Whats the integral of x^x and 1/(1+x^5) ?

Question

i tried searching in the internet for some formulas to do these to but to no avail. Tried substitution for the 2nd equation and it didn't work and the x^x has soo many controversies in the web that i dont even know whats the right answer =(.

kb · Accepted Answer

1) For x^x, there is no elementary antiderivative (even if you concern yourself with x > 0).
You can find series representatives for it though.

For example, ∫ x^x dx
= ∫ e^(x ln x) dx 
= ∫ [Σ(n = 0 to ∞) (x ln x)^n / n!] dx, and integrate this term by term using integration by parts.
-------------------------
2) This one is more tractable by (tedious) partial fraction computations.

Link:
http://www.wolframalpha.com/input/?i=integrate+1%2F%28x^5+%2B+1%29+dx

I hope this helps!

Anonymous · Answer

integral of x to the x is (1/(x+1) ) times x to the power of x+1

Anonymous · Answer

â« x^x dx is not integrable. 

Use trig sub for the other one.

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Whats the integral of x^x and 1/(1+x^5) ?

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