Question

Integrate:

Answer 1

\[(x+(1/x))^x\]

Answer 2

may i know the context/source of this problem ?

Answer 3

a friend gave it to me

Answer 4

i entered this on wolframalpha and this is what i got:-
http://www.wolframalpha.com/input/?i=integrate+%28x+%2B+%281%2Fx%29%5Ex++dx

Answer 5

@welshfella you put the wrong problem on wolfram. It is \( (x+(1/x))^x\)

Answer 6

\[f(x)=\left(x+\frac{1}{x}\right)^x\]?

Answer 7

Yea

Answer 8

and you want an "anti -derivative"?

Answer 9

the chances that you can find the closed form for this anti derivative seem very very small to me

Answer 10

@saumyawardhan1
Do you expect a closed form solution?
If you have a particular problem to solve, you can consider power series expansion or numerical integration.

Answer 11

The problem is of indefinite integral and the answer is in closed form.

Answer 12

Can you post the answer? It can help us tracing back to the way to get it.

Answer 13

You'll generally have a bad time trying to find a closed form for an antiderivative of \(f(x)^x\) if \(f\) is nonconstant.