Posted by **Jay** on Thursday, June 7, 2012 at 12:15am.

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)^2-tan^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))

- calculus (check my work please) -
**Bosnian**, Thursday, June 7, 2012 at 12:47am
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

- calculus (check my work please) -
**Jay**, Thursday, June 7, 2012 at 12:52am
I did, I got a completely different result. Also, SAY SOMETHING USEFUL NEXT TIME!!! tired of you spamming that stupid reply

- calculus (check my work please) -
**Bosnian**, Thursday, June 7, 2012 at 1:06am
Try to simplify your "different answers".

Probably your "different answers" is same solutions write in different form.

- calculus (check my work please) -
**Jay**, Thursday, June 7, 2012 at 2:19am
right, because my answer can be simplified into:

sec^5(x)/5-sec^3(x)/3

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