An idea for a video: Integrate ln(x)*x^(ln(x)-1)

Ian FowlerMay 13, 2020I started with integration by parts since int[ln(x)]dx = x[ln(x)-1] but didn't get very far. Nice problem. Thanks.

Charlie DrinnanMay 14, 2020Ultimately did it this way, but was after many attempts to make it work by integration by parts

Ian FowlerMay 14, 2020 · Edited: May 14, 2020@Charlie Drinnan I nearly **** (am I allowed to do that here?) my pants when I sawe^(x^2+2x+1) * (x+1). :)And when you move x^-1 in the denom and you see ln(x)/x with ln^2(x) in the exponent - same thing,

Charlie DrinnanMay 14, 2020Ha. Yeah, same boat. But, that eureka moment when you figure out the ln^2(x) insight is really nice.

I started with integration by parts since int[ln(x)]dx = x[ln(x)-1] but didn't get very far. Nice problem. Thanks.

Yeah. Seems like integration by parts would work.

Ultimately did it this way, but was after many attempts to make it work by integration by parts

@Charlie Drinnan I nearly **** (am I allowed to do that here?) my pants when I saw

e^(x^2+2x+1) * (x+1). :)

And when you move x^-1 in the denom and you see ln(x)/x with ln^2(x) in the exponent - same thing,

Ha. Yeah, same boat. But, that eureka moment when you figure out the ln^2(x) insight is really nice.