Why do logarithmic functions have absolute value signs after integration?

[pranjalverma]

Thank you very much for the great piece of explaination.This is often neglected in most of the textbooks .

[fikryizzudin]

I didn't search this video. This video came to me. And I am glad because it helped me understand one of the most thing that is often omitted or neglected.

[coolclips]

I was wondering about this for a while and I could never get a straight answer. Thanks for the great explanation

[code_explorations]

That's a great explanation of an interesting bit of maths I hadn't properly considered before. Thanks!

[mohfa]

brilliant...thank you very much for your great videos...i salute you

[sixtysixx]

Took me awhile to understand the reason of putting the minus in front of x. That is because log or ln cant take negative numbers, the only way to take negative numbers is do a double negative. Thx you are actually a unique and fancy teacher compared to Khan, all all other teachers online.

[kingofgoldnessr]

5:01 i like when he says "both" his hands are moving in the ln|x| shape

[hadrian]

It's wonderful when student behaviour is on point and teachers get to TEACH

[angelmendez-rivera]

The reason you should write ln|x| is because the derivative of ln|x| is indeed 1/x, and this is defined for all nonzero real x.

However, I should also mentioned that the full antiderivative of 1/x REALLY is ln|x| + Csgn(x) + D. This is due to the nonremovable discontinuity at x = 0. Technically, what should have been written in the board, ln(x) + C1 if x > 0, and ln(-x) + C2 if x < 0, and not necessarily assume C1 = C2.

[derontanzil]

i always thought that its cause 1/x dx can have many different solutions
for example, d/dx(ln(100x)) is just 1/x
hence, 1/x dx can be ln(ax) where a>0

[calyodelphi]

ln(-x) = ln(x) + iπ(2k+1) ∀ k ∈ Z

The log of a negative number just isn't a simple *real* number. It's a complex number. (Which I kinda personally love but hey that's just me.)

[James-wzxr]

Is it possible to understand this if you dont know calculus?