Here's what rhymes with inveatigating.
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gaping gauging engaging shaping escaping fading grading raging degrading lading shading evading raiding wading waging paging raping taping trading invading staging pervading scraping blockading parading braiding draping persuading upgrading cascading crusading reshaping disengaging downgrading upbraiding masquerading gaining gazing casing gaming caving making taking saying painting raising facing laying paying saving claiming failing naming sailing shaking weighing baking bathing grazing racing scaling waking wasting waving basing behaving chasing craving decaying delaying detailing fainting mailing pacing paving railing raining reigning shaving tasting wailing waning glazing raking raving regaining scathing whaling chafing chaining debasing detaining effacing erasing feigning hailing nailing pasting phasing quaking tailing taming veiling bailing basting baying bewailing craning declaiming faking graying haying hazing maiming neighing shaming waiving training breaking changing playing remaining placing prevailing ranging amazing pertaining praying retaining staying arranging attaining blazing engraving framing spacing staining tracing betraying blaming bracing draining flaming obeying praising swaying trailing braking phrasing slaying acquainting assailing availing awaking curtailing entailing flaking inhaling plaything preying staking allaying assaying braving braying buffeting defraying denaturing disclaiming disdaining flailing plaguing containing explaining obtaining replacing conveying displaying embracing modelling surveying campaigning exchanging proclaiming spraying straining appertaining appraising displacing exclaiming mistaking partaking retraining unfailing abstaining disobeying reclaiming refraining remaking renaming repaying straying unveiling inflaming ordaining retracing revelling strafing maintaining undertaking complaining entertaining sustaining ascertaining restraining unchanging portraying unavailing forsaking interlacing mainspring overtaking rearranging remodelling overgrazing constraining countervailing paraphrasing interchanging uncomplaining