Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

Americans pronounce investigate as ihn-VEH-stuh-gayt (/ɪnˈvɛstəˌɡeɪt/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "We'll investigate what went wrong" or "Thank you for your patience while we investigate this matter" — more examples below.
Record yourself saying "investigate" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 10 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Lift your bottom lip so its inner edge (where the wet part meets the dry part) touches the very bottom of your top front teeth. Add vocal cord vibration as you blow air through.

Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Raise the back of your tongue to touch the soft palate. Add vocal cord vibration, then release.

Start with your jaw slightly open and the front of your tongue forward and slightly up. Glide upward, your jaw closes a little more and your tongue arches higher toward the roof of the mouth.
Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

Click any sentence to see the full breakdown — every link, every reduction, every flap-T.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "investigate", the "t" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the second syllable, not the others. Stretch VEH — keep everything else short and quick.
Don't pronounce the second syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.