Integrate sec(x)^4

Just making sure this is right...
I got
tan(x)sec(x)^2 - (2/3) tan(x)^3 + C

Question

Integrate sec(x)^4

Just making sure this is right... 
I got 
tan(x)sec(x)^2 - (2/3) tan(x)^3 + C

kinggeorge · Answer

although, if you integrate it you do get sec(x)^4, so I guess it should be right.

kinggeorge · Answer

I mean derive it. Not integrate it.

anonymous · Answer

okk.. I used integration by parts.. but I also doubled checked with substitution and I got a different answer...

kinggeorge · Answer

I've checked with wolfram, you probably got a different form, but it is correct.

anonymous · Answer

oh okk thank you!

kinggeorge · Answer

$${1 \over 3} (\cos(2 x)+2) \tan(x) \sec^2(x)+C$$is the original answer wolfram gave me, but it's equivalent to your initial solution.

anonymous · Answer

thank you!! would you be able to look at another question? I've asked around and no one seems to have any idea....

kinggeorge · Answer

sure

anonymous · Answer

thank you.. let me post the link here...

anonymous · Answer