Integral ∫(1/2x)dx

  • Thread starter johann1301
  • Start date
  • #1
217
1

Homework Statement



∫(1/2x)dx

The Attempt at a Solution



I factor out (1/2) and i get ∫(1/2x)dx=(1/2)ln|x|+C
∫(1/2x)dx
(1/2)∫(1/x)dx
(1/2)ln|x|+C

But cant i say that u=2x and dx=du/2 and get ∫(1/2x)dx= (1/2)ln|2x| + C
∫(1/2x)dx
u=2x
∫(1/u)(du/2)
∫(1/2u)du
(1/2)∫(1/u)dx
(1/2)ln|u| + C
(1/2)ln|2x| + C

if i can do this, i get two different answers...

can i use the last method?
 

Answers and Replies

  • #2
Ibix
Science Advisor
Insights Author
2020 Award
7,384
6,468
ln 2x = ln x + ln 2. One of your C constants is equal to the other plus ln 2.

Both your answers are right...
 
  • Like
Likes 1 person

Related Threads on Integral ∫(1/2x)dx

  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
12
Views
20K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
2K
Replies
6
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
134K
Replies
4
Views
2K
  • Last Post
Replies
4
Views
9K
Top