Struggling with Finding the Anti-Derivative of (4+u)/u?

[kemmy]

Homework Statement

Find the anti-derivative: \int[(4+u)/u]du

The Attempt at a Solution

I've tried a couple different ways to find this anti-derivative and I know I keep missing something.
I tried to split it up into \int(4+u)(u^-1)du
but then I think I do something wrong because I end up getting 4ln|u|.

Any help you could give would be much appreciated- I've tried this problem so many times and I just can't figure out what I'm missing. Thanks.

 

[PingPong]

Try breaking up your numerator (i.e. (a+b)/c = a/c + b/c).

 

[kemmy]

Thanks. I just tried that, and it helped a little- but I'm still getting the wrong answer, according to the textbook.

so I split the equation up into [(4/u)+(u/u)] then I rewrote that to [(4)(1/u) + (u)(1/u)]
from that I got 4ln|u| + (1/2)(u^2) ln|u|. What am I still doing wrong??

If anyone could set me on the right path, that would be fantastic, thanks.

 

[PingPong]

Be careful! (u)(1/u)=1, not u^2.

 

[Ithryndil]

The first part of your answer looks fine. Why did you change u/u into u(1/u)? Before integrating what does u/u equal?

 

[kemmy]

Oh! I think I've got it...
so 4+u/u to (4/u)+ (u/u) to 4(1/u)+(u/u) cancel out the u/u to equal 1 and turn it to
4ln|u|+x+c.
right?
Thanks for all the help!

 

[PingPong]

Right! Just one minor point, you're integrating with respect to u, so it's actually 4 ln |u| + u, not x :)

 

[kemmy]

Ack! okay...I think I can remember to catch that u.
Thanks so much for all your help!