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This is a trigonometric integration using trig identities.

S tanX^3 secX dX

S tanX^2 secX tanX dX

S (secX^2 -1) secX tanX dX

u = secX

du = secX tanX

S ( u^2 - 1) du

1/3secX^3 - secX + C

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Q: What is the integral of tan cubed x secx dx?
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What is the integral of tanx times sqrt secx dx?

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