## anonymous 4 years ago Integration problem: If I Integrate this $\ \int\frac{y}{(y+1)^2}dy$ using integration by parts I get:$\frac{-y}{y+1}+ln(y+1)$ but if I do this: $\ \int\frac{y}{(y+1)^2}dy$ $\ \int\frac{y+1}{(y+1)^2} -\frac{1}{(y+1)^2}dy$and integrate I get $\ \frac{1}{y+1} +ln(y+1)$ Sooo, what did I do wrong, what am I missing?

1. anonymous

Dude can't you see both are one and the same thing

2. anonymous

Write -y as -y+1-1 see

3. anonymous

the second one is correct

4. lalaly

id prefer to use partial fractions or the second method u used

5. anonymous

no need for integration by parts here

6. anonymous

Just add constant of integration to both you would be surprised that after carring out what i just said you find same function with different constant of integration.... A result is consistent with what you expect out of an indefinite integration

7. anonymous

Method never changes the result it just changes the convinence of solving...

8. anonymous

Ah yes, thank you very much, this is actually a part of a bigger problem (a differential equation with given initial conditions) I didn't get the same constant C for the particular solution so i got confused, but it all works out nicely :D.

9. anonymous

"I didn't get the same constant C" like they got in the book.

10. anonymous

you said it's part of a bigger problem...my instructor spent 30 min today stressing on the importance of adding the C right away cuz waiting til the end will change it completely. for ex: dy/dx=y...add C right away and you get y=Ce^x instead of y=e^x+C