Wavetable synthesis is a popular sound synthesis method enabling the efficient creation of musical sounds. Using sample rate conversion techniques, arbitrary musical pitches can be generated from one wavetable or from a small set of wavetables: downsampling is used for raising the pitch and upsampling for lowering it. A challenge when changing the pitch of a sampled waveform is to avoid disturbing aliasing artifacts. Besides bandlimited resampling algorithms, the use of an integrated wavetable and a differentiation of the output signal has been proposed previously by Geiger. This paper extends Geiger’s method by using several integrator and differentiator stages to improve alias-reduction. The waveform is integrated multiple times before it is stored in a wavetable. During playback, a sample rate conversion method is first applied and the output signal is then differentiated as many times as the wavetable has been integrated. The computational cost of the proposed technique is independent of the pitch-shift ratio. It is shown that the higher-order integrated wavetable technique reduces aliasing more than the first-order technique with a minor increase in computational cost. Quantization effects are analyzed and are shown to become notable at high frequencies, when several integration and differentiation stages are used.