Problem with Wolfram's online integrator

[BenVitale]

I tried to do integral[cos(x)]^x dx

but Wolfram's online integrator reported that it couldn't do it

Am I missing something?

 

[Dale]

From your syntax it is not clear if you want to take the integral of cos(x)^x or if you want to take the integral of cos(x) and then raise that to the power of x. If it is the first then there is probably no known closed form solution for that integral.

 

[dE_logics]

Wolfram is not that good.

Try www.quickmath.com, it's better; or if you're on Linux, there're plenty of computer algebra systems.

However this time quickmath also failed...very hilarious answer.

I tried it in axiom, and the answer is bad -

$$\int \sp{\displaystyle x} {{{\cos \left( { \%M} \right)} \sp \%M} \ {d \%M}}$$

yacas gives the same results (as quickmath).

sympy takes infinite time to solve (as with most complex cases)

So I conclude there's something wrong with the question itself.

 

[BenVitale]

From your syntax it is not clear if you want to take the integral of cos(x)^x or if you want to take the integral of cos(x) and then raise that to the power of x.
.

It's taking the integral of cos(x)^x

So I conclude there's something wrong with the question itself.

Maybe, maybe not. I thought of a manipulation:

I figure that for all values of x, cos x will fall in [-1,+1].
So, taking the integral of cos(x)^x is equivalent to taking the integral of x^x over [-1,0] and [0,+1]

What do you think?

 

[Dale]

By that logic the integral would be the same as sin(x)^x or frac(x)^x or saw(x)^x or any other function bounded between -1 and 1.

 

[BenVitale]

By that logic the integral would be the same as sin(x)^x or frac(x)^x or saw(x)^x or any other function bounded between -1 and 1.

Oh, yes. I see your point. I'm at loss here. What do you suggest?

 

[Hepth]

use wolfram alpha, but you need the correct syntax.

http://www.wolframalpha.com/input/?i=Integrate[Cos[x]^2,x]

 

[BenVitale]

use wolfram alpha, but you need the correct syntax.

http://www.wolframalpha.com/input/?i=Integrate[Cos[x]^2,x]

Well, that is the result for integrate[Cos[x]^2,x]

I was looking for a result for the indefinite integral : Integrate[Cos[x]^x,x]

 

[Dale]

I believe there is no closed form for this integral. You will have to evaluate it numerically.