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int sec^(3) x dx...

`int sec^(3) x dx`

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Let `I=int sec^(3)x dx " d"=int secx sec^(2)x dx`
`=int sqrt(1+tan^(2)x)sec^(2)x dx`
Put `tan x=z " and " sec^(2)x dx=dz`
` :. I=int sqrt(1+z^(2))dz`
`=(zsqrt (z^(2)+1))/(2)+(1)/(2)log|z+sqrt(z^(2)+1)|+C`
` =(tanx sec x)/(2)+(1)/(2)log|tanx +secx| +C`
`=(1)/(2)[secx tanx + log|secx +tanx|] +C`
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