Mathematics

Evaluate :  $$\int \frac { \sec x d x } { \log ( \sec x + \tan x ) }$$


SOLUTION
Let $$I=\int \cfrac{\sec xdx}{\log(\sec x+\tan x)}$$
Let, $${\log(\sec x+\tan x)}=z$$
$$\implies \sec xdx=dz$$
So, $$I=\int\cfrac{dz}{z}=\log z+c$$
Hence $$I=\log({\log(\sec x+\tan x)})+c$$
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Subjective Medium Published on 17th 09, 2020
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