Answer to Question #332665 in Calculus for Olga

Question #332665

Determine the following integral

∫  (1+cos^2 x  / 1+cos 2x ) dx



a.    1 / 2 [ tan x + x] + c


b.   1 / 2[1− 1 / cos x ] + c


c.    1 / 2 + c


d.   1 / 2 tan x + x + c



1
Expert's answer
2022-04-27T17:20:08-0400
1+cos2x1+cos2xdx=1+cos2x2cos2xdx\int \dfrac{1+\cos^2x}{1+\cos2x}dx=\int \dfrac{1+\cos^2x}{2\cos^2x}dx

=121cos2xdx+12dx=\dfrac{1}{2}\int \dfrac{1}{\cos^2x}dx+\dfrac{1}{2}\int dx

=12(tanx+x)+C=\dfrac{1}{2}(\tan x+x)+C

a. 12(tanx+x)+C\dfrac{1}{2}(\tan x+x)+C


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