This is the simple version of a white LED lamp that can be directly powered from mains.
It can give ample light even for reading purpose. Capacitor Cx along with diodes D1 through D4 forms the AC step down circuit. Cx reduces high voltage AC from mains to a low voltage AC which is rectified by the bridge diode.
Capacitor C1 removes ripples from AC so that low voltage DC is available to power the LEDs. Cx is the X rated AC capacitor that reduces AC voltage through capacitive rectance property. Resistor R1 is very important to remove the stored voltage from Cx when power is switched off. This prevents lethal shock.
Resistor R2 limits the inrush current.
More LEDs can be added by reducing the value of R2.Since the circuit is directly connected to mains, take utmost care to avoid shock. No components should be touched when it is connected to mains.