October 26, 2016

Homework Help: Integration

Posted by Vidal on Sunday, October 15, 2006 at 2:06am.

Intergrate sec^3(x) dx

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

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

[3x sin x/cos^4(x)] dx
= -3 [x/cos^4(x)] d cos x
= x d sec^3(x)
= x sec^3(x) - 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 sec3(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.

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