How to determine ∫x^xdx ?

[duron999]

How to determine .......

what is the answer ???
please show the step, thanks !

 

[dazhen]

Re: How to determine .......

See the solution attached.

 

[cedance]

Re: How to determine .......

See the solution attached.

i think the one u wrote is not right..

d(x^x) = x * x^(x-1) + x^x * log(x)

u applied only the x^n rule... what abt n^x rule? where n is constant.. u have to assume both the rules i mean... assuming x in the base as constant and x in the power as constant... and

to my knowledge, there s no answer for it. there are no integral s that exist for functions that osciallate too much or diverge at very faster rates.. if u could plot the function using matlab or mathematica or maple, then u could see how fast it diverges. i have read this in "fundamentals of calculus" by thomas and finney.

/Am

 

[dazhen]

Re: How to determine .......

See the solution attached.

i think the one u wrote is not right..

d(x^x) = x * x^(x-1) + x^x * log(x)

u applied only the x^n rule... what abt n^x rule? where n is constant.. u have to assume both the rules i mean... assuming x in the base as constant and x in the power as constant... and

to my knowledge, there s no answer for it. there are no integral s that exist for functions that osciallate too much or diverge at very faster rates.. if u could plot the function using matlab or mathematica or maple, then u could see how fast it diverges. i have read this in "fundamentals of calculus" by thomas and finney.

/Am

Yes, I think you're right about it.

 

[duron999]

Re: How to determine .......

See the solution attached.

i think the one u wrote is not right..

d(x^x) = x * x^(x-1) + x^x * log(x)

u applied only the x^n rule... what abt n^x rule? where n is constant.. u have to assume both the rules i mean... assuming x in the base as constant and x in the power as constant... and

to my knowledge, there s no answer for it. there are no integral s that exist for functions that osciallate too much or diverge at very faster rates.. if u could plot the function using matlab or mathematica or maple, then u could see how fast it diverges. i have read this in "fundamentals of calculus" by thomas and finney.

/Am

someone told me that x^x = e^(xlnx) , can i find solution ???

 

[arunragavan]

Re: How to determine .......

i think this is how it goes..
lemme give it a shot..

x^x = e ^ (xlogx)

here (xlogx) = LOG (x^x)

x^x = e ^ log (x^x)

let (x^x) = y

x^x= e log

= y

therefore

x^x = y = x^x

this is wot i guess u want to conclude with..

confused :d

anyway with regards,

 

[hwswboy]

Re: How to determine .......

Don't waste your time,this is an expression that is notorious for not having a closed form solution.

This function does not have an elementary integral, just as e^(x^2) and sin(x)/x do not.

Yo can stimate it using Riemann sums, Simpsons method or any standard method of numerical integration.

 

[mmatica]

Re: How to determine .......

"there are no integral s that exist for functions that osciallate too much or diverge
at very faster rates.. if u could plot the function using matlab or mathematica or maple, then u could see how fast it diverges. i have read this in "fundamentals of calculus" by thomas and finney. "

This is not true! x e^(x^2) is growing more quickly than x^x and it has an elementary antiderivative!

M.

 

[cedance]

Re: How to determine .......

"there are no integral s that exist for functions that osciallate too much or diverge
at very faster rates.. if u could plot the function using matlab or mathematica or maple, then u could see how fast it diverges. i have read this in "fundamentals of calculus" by thomas and finney. "

This is not true! x e^(x^2) is growing more quickly than x^x and it has an elementary antiderivative!

M.

i might not have put the words properly which is so important for math! i remember having seen 3 conditions for an integral not to exist. dont remember them exactly. will reply with those points again!

/Am