# Intergrate ¡ì sec^3(x) dx

could anybody please check this answer. are the steps correct? thanks.

= ¡ì sec x d tan x

= sec x tan x - ¡ì tan x d sec x

= sec x tan x - ¡ì sec x tan^2(x) dx

= sec x tan x + ¡ì sec x dx - ¡ì sec^3(x) dx

= sec x tan x + ln |sec x + tan x| - ¡ì sec^3(x) dx

=¡ì sec^3(x) dx = (1/2)(sec x tan x + ln |sec x + tan x|) + C1

¡ì [3x sin x/cos^4(x)] dx

= -3 ¡ì [x/cos^4(x)] d cos x

= ¡ì x d sec^3(x)

= x sec^3(x) - ¡ì sec^3(x) dx

= x sec^3(x) - (1/2) sec x tan x - (1/2) ln |sec x + tan x| + C2

I'm not sure if your integration is correct or not, not all of your symbols converted to ASCII. I plugged sec^{3}(x) into a piece of software and got an answer that looks slightly different from yours, but I'm not positive. If you still need help with this post a new question so it's easy to find.