Q: what is the best way to back up my macbook without an external hardrive

Something like or similar to Carbonite.

If your Mac isn't available any longer whatever the reason, you may wish to have a recent backup available. So it's a good idea to backup on an external device, as it may be detached from your Mac if it's stolen.

If you have other methods, as a NAS or a server you trust, you can backup on these devices.

If you have few datas, you can save to a DVD.

You can save datas on iCloud or other cloud services.

But I'd advise you against any backup on your main disk.

I agree with RégisfromFr.  Backups to external HDs are the safest and most reliable backups. You can clone your MBP to the EHD with Carbon Copy Cloner or SuperDuper and update it on a weekly basis.  This will make you your Macbook Pro available in case it's stolen by connecting the EHD to another Mac and booting from the drive. 

The drive can be kept separate from the MBP in a safe place. My wife uses this EHD for her clone: OWC Mercury On-The-Go Pro USB 3.0 & 2.0 / FireWire 800, and 2.5" SATA Portable External Hard Drive & SSD

There's no cloud backup that can handle iPhoto libraries if you have one and value your pictures. Cloud backups and take days to recover as they often limit the download speed available.

If you value your data it's best to have two independent backups of your MBP hard drive: a clone and a Time Machine backup.

OT

As Lanny says, Carbonite, Mozy, CrashPlan, SugarSync, etc...  You do pay a monthly fee for the storage, and it does take a long time to get the data copied over the net initially, but then only backups the changes.  Restoring can be back over the net, or some of them offer a service to ship you a disk with your data on it (for a fee).

You could get an Apple Time Capsule and use Time Machine to backup over your home network to the Time Capsule.  Since this is on your home LAN, transfer times will be much faster.  The first backup is best if you connect your Mac via an ethernet cable to the Time Capsule, as that would be faster, but then you can continue doing incremental backups via WiFi.

If you have another system in your house (such as an iMac, Mac mini, or a laptop that does not move around and can have external drives attached, or even a Windows PC), then you could use CrashPlan (the free option) to backup from your Macbook Pro to that other system.

CrashPlan can even be used to backup to another computer at a family member's house, or a friends, again for free (except for your networking costs).

You could also get a NAS in your home, and backup to that (similar to a Time Capsule in concept).