A) \[{{e}^{x}}.secx+c\]
B) \[{{e}^{x}}.tanx+c\]
C) \[{{e}^{x}}.se{{c}^{2}}x+c\]
D) \[{{e}^{x}}+tanx+c\]
Correct Answer: B
Solution :
[b] \[I=\int {{e}^{x}}.(\tan x+{{\sec }^{2}}x).dx={{e}^{x}}.\tan x+c\] \[\left[ \because \int {{e}^{x}}.\left( f\left( x \right)+f'\left( x \right) \right)dx={{e}^{x}}.f\left( x \right)+c \right]\] Hence, option [b] is correct.
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