calculus (check my work please)
posted by Jay .
Not sure if it is right, I have check with the answer in the book and a few integral calculators but they seem to get a different answer
∫ sec^3(x)tan^3(x) dx
∫ sec^3(x)tan(x)(sec^2(x)1) dx
∫ tan(x)sec(x)[sec^4(x)sec^2(x)] dx
∫ tan(x)sec(x)[(tan^2(x)+1)^2tan^2(x)1] dx
∫ tan(x)sec(x)(1+2tan(x)+tan^2(x)tan^2(x)1) dx
∫ 2tan^2(x)sec(x) dx
∫ 2(sec^2(x)1)sec(x) dx
∫ 2sec^3(x)2sec(x) dx
2∫ sec^3(x) dx 2∫ sec(x) dx
*reduction formula
2tan(x)sec(x)ln(tan(x)+sec(x))

In google type:
wolfram alpha
When you see lis of results click on:
Wolfram Alpha:Computational Knowledge Engine
When page be open in rectangle type:
integrate sec^3(x)tan^3(x) dx
and click option =
After few secons you will see result.
Then click option Show steps 
I did, I got a completely different result. Also, SAY SOMETHING USEFUL NEXT TIME!!! tired of you spamming that stupid reply

Try to simplify your "different answers".
Probably your "different answers" is same solutions write in different form. 
right, because my answer can be simplified into:
sec^5(x)/5sec^3(x)/3