Do I need a phono amp if I own an integrated amp?

If the integrated amp has 'phono' inputs, then yes. The amp will have a source selector switch on the front - if one of the selections is 'phono' - then yes, hook the turntable to the input labled Phono in the back (only use this jack for your turntable)

Some integrated amps have a phono stage, others do not, even within the same brand/model. Many times it is an add-on; you may find the same amplifier, one with phono, one without.

It is not hard to add phono even if your amplifier does not have phono built in. You can buy an external phono stage preamp for as little as $30. (You can also spend thousands$).

Take a look at some inexpensive ones here that would be fine for a beginner audiophile quality turntable.

Phono Stage Preamps

You can find used ones for a lot less on AudiogoN and on eBay.

The AudiogoN classified link is here ..

Phono Stage Preamps

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The 'phono amp' is an RIAA equalization and step-up stage that must take place with phono cartridge signals. Many integrated amplifiers have this built in to them. Your instruction manual or the dealer should be able to verify this for you.