Can you please explain what did my professor do in this problem? At that time I can't attend his online lecture due to power outage in our area. So can you help me understand this problem? sin x- sin xdxcos3:dxtan xdxCOS X -cos x16.dxsec x dx +cos? xcoS Xcos? xLet u = cos x ; du = – sin x dx-2CoScos 2 x+ C-2= In|sec x + tan x|++ CIn|sec x + tan x|+-2= In|sec x + tan x| – sec? xsec2 x + C--

It is given that ∫cosx-tanxcos2x dx We have to evaluate it.

sin x cos x – tan x cos² x dx cos x cos? x sin x dx cos3 x 16. = sec x dx + cos x Let u = cos x ; du - sin x dx cos-2 x -2 CoS = In|sec x + tan x|+ + C = In|sec x + tan x|+ -2 + C -2 1 = In|sec x + tan x| - sec? x

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 22E

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Question

Can you please explain what did my professor do in this problem? At that time I can't attend his online lecture due to power outage in our area. So can you help me understand this problem?

sin x
- sin x
dx
cos3:
dx
tan x
dx
COS X -
cos x
16.
dx
sec x dx +
cos? x
coS X
cos? x
Let u = cos x ; du = – sin x dx
-2
CoS
cos 2 x
+ C
-2
= In|sec x + tan x|+
+ C
In|sec x + tan x|+
-2
= In|sec x + tan x| – sec? x
sec2 x + C
--

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