When you integrated 1/x with IBP, you left out the absolute value with the ln. Your answer is only true if x>0 and that is the issue I have with the solution.
❤ I = integral of (1/x - ln x)/e^x now we have to put denominator in squared form I = integral of { e^(x) (1/x) - ln x (e^x) } e^(2x) I = (ln x)/(e^x) + c
When you integrated 1/x with IBP, you left out the absolute value with the ln. Your answer is only true if x>0 and that is the issue I have with the solution.
that wwas smoth, and im proud i could solve it before seeing the video !
❤
I = integral of (1/x - ln x)/e^x
now we have to put denominator in squared form
I = integral of { e^(x) (1/x) - ln x (e^x) } e^(2x)
I = (ln x)/(e^x) + c
Quotient rule in reverse
Integration by parts is usually derived from product rule but there exists version from quotient rule