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Integrate the following functions: tan^3...

Integrate the following functions: `tan^3 2x sec(2x)`

Text Solution

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`tan^3 2x sec 2x = tan^2 2x sec 2x tan 2x`
= (sec^2 2x-1) sec 2x tan 2x`
Put t = sec 2x
Then dt = 2 sec 2x tan 2x dx
`gt sec 2x tan 2x = dt/2
therefore `int tan^3 2x sex 2x dx = `int (t^2-1) dt/2`
=1/2[t^3/3-t]+c`
=`1/2[(sec^3 2x)/3 - sec2x]+c`
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