Thread: Who is familiar with Pythagoras?

The integral of x^x dx. I like a good puzzle,...sets my mind working.

Ok...x^x needs to be expressed as a Power Series. As I mentioned above,..express x^x as e^xlnx and then using the Maclaurin Series for e^x expand e^xlnx. In closed form this is the summation from n = 0 to infinity of (x^n(lnx)^n)/n!. This expression can be integrated term by term and there is a considerable quantity of work to cover in order to obtain the solution.

Limits are set from 0 to 1 and the integral of x^x dx is finally shown to be the summation from n = 1 to infinity of (-1)^n-1/n^n

Ron.

Originally Posted by slug_burner

What has Industrial Design got to do with mathematics anyway?

Not a lot, but we use basic geometry a bit...ID comes under the school of engineering at UWS and every engineering student has to do maths. Year 12 maths wasn't even a prerequisite when I started the degree!

Originally Posted by RoverP6B

The integral of x^x dx. I like a good puzzle,...sets my mind working.

Ok...x^x needs to be expressed as a Power Series. As I mentioned above,..express x^x as e^xlnx and then using the Maclaurin Series for e^x expand e^xlnx. In closed form this is the summation from n = 0 to infinity of (x^n(lnx)^n)/n!. This expression can be integrated term by term and there is a considerable quantity of work to cover in order to obtain the solution.

Limits are set from 0 to 1 and the integral of x^x dx is finally shown to be the summation from n = 1 to infinity of (-1)^n-1/n^n

Ron.

just did that in class

Originally Posted by schmierer LR at singleton

just did that in class

i use to be quite good at maths at one stage i was ranked 96th in the state which was out of 16500 students oh how things have changed