integral of dx/(50-10x)

Question

If ∫dx/(50-10x)=1/10∫dx/(5-x) 

 

∫dx/(50-10x)

 

u=50-10x du=-10dx  dx=du/-10  -1/10∫du/u=-1/10ln[50-10x]+c

 

1/10∫dx/(5-x)

 

  u=5-x  du=-1dx dx=-du -1/10∫du/u=-1/10ln[5-x]+c

 

If the integrals are equivalent,why are the answers not the same?

 

 

Answer 1

Wally, 

 

Why didn't you answer as a comment when I asked your concern when you posted this question previously.

 

In your first answer above ln(50-10x) = ln[10(5-x)] = ln(10)+ln(5-x).

 

When you multiply this by (-1/10) the  (-1/10)ln(10) is a constant and just becomes part of c in your second answer; remember c is just an arbitrary constant.

 

Does that answer your question?