A) \[\log (\cos x+\sin x)+c\]
B) \[\log ({{\sec }^{2}}x)+c\]
C) \[\log (1+\tan x)+c\]
D) \[-\frac{1}{{{(1+\tan x)}^{2}}}+c\]
Correct Answer: C
Solution :
Put \[t=1+\tan x\Rightarrow dt={{\sec }^{2}}x\,dx\] \[\int_{{}}^{{}}{\frac{{{\sec }^{2}}x}{1+\tan x}}\,dx=\int_{{}}^{{}}{\frac{1}{t}\,dt=\log t+c}\]\[=\log (1+\tan x)+c.\]
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