A) \[{{e}^{x}}\sin x+c\]
B) \[{{e}^{x}}\cos x+c\]
C) \[{{e}^{x}}\tan x+c\]
D) \[{{e}^{x}}\sec x+c\]
Correct Answer: C
Solution :
\[I=\int{{{e}^{x}}(1+\tan x+{{\tan }^{2}}x})dx\] Þ\[\int{{{e}^{x}}(1+\tan x+{{\tan }^{2}}x)dx=\int{{{e}^{x}}(\tan x+{{\sec }^{2}}x)}\,dx.}\] \[I={{e}^{x}}\tan x+c\] \[(\because \,\int{{{e}^{x}}[f(x)+{f}'(x)]+x={{e}^{x}}f(x)+c}).\]
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