Why there is no decoupling capacitors in analog IC
Decoupling capacitors are used in digital circuits to suppress the high-frequency noise generated on the supply line (Vcc or Vdd) as a result of the rapid switching inside the chip. The signals that are switching are usually square waves, which generate a lot of harmonics.

These capacitors fulfill dual roles -- they provide a little energy reserve to suppress voltage spikes inside an IC, and they help suppress any voltage spikes on the supply line outisde the chip from getting in.

Analog circuitry, on the other hand, usually doesn't switch as fast as digital IC's do, and even when it does, the signals usually aren't square waves so they don't have as many harmonics.  Still, it is recommended to put decoupling IC's on all analog chips like op-amps.  They are especially  needed for analog devices that have a poor power supply rejection ratio (PSSR) to avoid power supply fluctuations from affecting the output.

In either case, decoupling caps are almost never found inside the IC's; as others have pointed out, they are usually separate components placed next to a chip between the power and ground pins.  Values of 100 nf (0.1 µF) and 10 nf (0.01 µF) are often used.

Decoupling caps are required to not only make your circuit behave more reliably, but also to reduce emissions to enable it to pass FCC certification.