How to determine ∫x^xdx ?

dazhen said:

See the solution attached.

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arunmit168 said:

dazhen said:

See the solution attached.

Click to expand...

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

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arunmit168 said:

dazhen said:

See the solution attached.

Click to expand...

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

Click to expand...

mmatica said:

"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.

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