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Question
Find the integrals of the function:
tan3 2x sec 2x
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Solution
Let `I = int tan^3 2x sec 2x dx`
`= int tan^2 2x * tan 2x * sec 2x dx`
`= int (sec^2 2x - 1)* sec 2x tan 2x dx`
Put sec 2x = t
⇒ 2 sec 2x tan 2x dx = dt
∴ `I = 1/2 int (t^2 - 1) dt 1/2 (t^3/3 - 1) + C`
`= 1/6 sec^3 2x - 1/2 sec 2x + C`
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