Integrate: find int [ y / (y + 1) ] dy (calc ans not same as

[moy1989]

Hey guys, I ran into this problem that I am unable to get the right answer to. My problem is that I cannot get the answer to the following integral:

int( y / (y+1) dy )

This is what I did...

I used integration by parts method

u = y du = dy
dv = 1 / (y+1) dy v = ln(|y+1|)

u * v - int( v * du )

y * ln(|y+1|) - int( ln(|y+1|) dy )

I'm not sure, but I think y * ln( |y+1| ) somehow becomes y * ln( y+1 ) and int( ln(|y+1|) dy ) somehow becomes int( ln( y+1 ) dy ); correct me if I'm wrong.

y * ln( y+1 ) - ( (y+1) * ln( y+1 ) - (y+1) )

After simplification I attained the answer

(y+1) - ln( y+1)

as opposed to the answer my calculator gives me

y - ln( |y+1| )

I don't know where I go wrong

 

[royhaas]

Re: Integrate

Your answer appears to differ from the calculator by a constant, which is not unexpected for an anti-derivative, i.e., an indefinite integral. Also note that the original integrand can be written as \(\displaystyle 1-\frac{1}{y+1}\), so that integration by parts isn't necessary.

 

[moy1989]

Re: Integrate

thanks royhaas

 

[stapel]

Note: If you use the poster's suggested reformatting, you will get the calculator's form of the answer (that is, the form without the "+1" outside the log). :idea:

And, technically, the integral of 1/x is supposed to involve absolute-value bars (though we all tend to leave them off), so the calculator's answer is "more correct" in that respect. :wink:

Eliz.