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Integrate the functionstan^3 2xsec2x...

Integrate the functions`tan^3 2xsec2x`

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`" Let " I= int tan^(3) 2x. sec 2x dx`
` = int (tan^(2) 2x). (tan 2x) . sec 2x dx`
` = int (sec^(2) 2x-1). (tan 2x. sec 2x) dx`
`underset( rArr sec 2x . tan 2x dx =(dt)/(2))underset(rArr 2 sec 2x. tan 2x =(dt)/(dx))(" Let " sec 2x=t)`
` :. I = int (t^(2) -1) (dt)/(2)`
` =(1)/(2) [(t^(3))/(3) -t]+c`
` =(1)/(6) sec^(3) 2x -(1)/(2) sec 2x+c`
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