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Integrate the functionstan^4x...

Integrate the functions`tan^4x`

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` int tan^(4) x dx`
` = int tan^(2) x. tan^(2) x dx`
`= int tan^(2) x. (sec^(2) x-1) dx`
` = int tan^(2) x. sec^(2) x dx`
` - int tan^(2) x dx " " underset(rArr sec^(2) x dx =dt)(" Let " tan x=t)`
` = int t^(2) dt - int (sec^(2) x-1)dx`
`=(1)/(3)t^(3) -tan x+x+c`
`=(1)/(3) tan^(3) x-tan x+x+c`
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