Question

Medal for answer: What's the difference between these integrals? (why not the same?)

Answer 1

they are the same, you just wrote them differently

Answer 2

@oshrinuri
This is a repeat of your earlier post.

Wolfram gives BOTH integrals as
-1/4 ln (2x-1)

I suggest you check the method.for the right hand column

@TuringTest I graphed both his integral - they are not the same as written

Answer 3

I'm really confused. What's wrong with the right column? I factored out -0.25 to get an integral of f'(x)/f(x)

Answer 4

symbolab.com gives different answers..

Answer 5

on your second to last step on the left you can do\[-\frac12\cdot\frac12\int\frac2{2x-1}dx=-\frac14\int\frac2{2x-1}dx\cdot\frac22=-\frac14\int\frac4{4x-2}dx\]and now you have the integral on the right
why they are not the same graph i don't know yet

Answer 6

they are the same, you just need to use the constant

Answer 7

No - one has asymptote at x= 0.5, other has asymptote at x=1

Answer 8

\[0.25\ln|4x-2|=0.25\ln2+0.25\ln(2x-1)+C=0.25\ln(2x-1)+C\]

Answer 9

they only differ by a constant

Answer 10

oops absolute value but you get the idea

Answer 11

\[0.25\ln|4x-2|=0.25\ln2+0.25\ln|2x-1|+C=0.25\ln|2x-1|+C\]

Answer 12

Anyway, both of the answers are right?

Answer 13

yes, and they both have an asymptote at 0.5

Answer 14

+C can absorb other constants, so if your answers to indefinite integrals seem different, they should only differ by a constant

Answer 15

I understand. Thanks to both of you!

Answer 16

Oops - and apologies for leading you astray @oshrinuri

Answer 17

welcome!

Answer 18

I think they are different. on the right when you factored out 1/4 that would be incorrect because you did not have 8 to start with

Answer 19

is that u or 4 anyway?