Integral of sec^3(x) without reduction (1 Viewer)

[jjjcjjj892]

Can anyone help me integrate sec^3(x) without using the reduction formula?

 

[Drongoski]

do you allow integration by parts?

 

[jjjcjjj892]

Yea no problem, only issue I have is with just going straight to a reduction formula, I want to see how the answer progresses to the solution rather than going from a -> b.

 

[Drongoski]

I think you can do it this way with IBP:

 

[Paradoxica]

Alternatively you can differentiate sec³x and then rearrange both sides and re-integrate. However this is essentially the same as Integration By parts.

 

[InteGrand]

"Inspection"

 

[jjjcjjj892]

I think you can do it this way with IBP:

Thanks for the reply, the way I progressed was going:



And its at this point I get lost, I can get the sec integral fine, its given, but the integral is confusing

 

[Squar3root]

Thanks for the reply, the way I progressed was going:



And its at this point I get lost, I can get the sec integral fine, its given, but the integral is confusing

use the identity tan^2(x) = sec^2(x) - 1

 

[Squar3root]

Spoiler

 

[Squar3root]

that spoiler was a fail

 

[jjjcjjj892]

Spoiler

Thank you, that made it very clear cheers everyone for the help.