The best replacement for integrals is derivatives.

The best alternatives to integrals are rated as following:
★★★★★  derivatives
★★★★  double integrals
★★★★  definite integrals
★★  summation
★★  triple integrals
★  indefinite integrals
★  indefinite

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Speaking about integrals, one probably shouldn't forget about absolute values.

Other search terms related to integrals and their ratings are:
★★★★★ absolute values
★★★★ absolute value
★★★ substitution
★★ trig substitution
★ u substitution
★ partial fractions
★ inverse trig
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