A) \[{{e}^{x}}\cos e{{c}^{-1}}x+C\]
B) \[{{e}^{x}}{{\sin }^{-1}}x+C\]
C) \[{{e}^{x}}{{\sec }^{-1}}x+C\]
D) \[{{e}^{x}}{{\cos }^{-1}}x+C\]
Correct Answer: A
Solution :
[a] : Since \[\int_{{}}^{{}}{{{e}^{x}}(f(x)+f'(x))dx={{e}^{x}}f(x)+C}\] \[\therefore \]\[\int_{{}}^{{}}{{{e}^{x}}\left( \cos e{{c}^{-1}}x+\frac{(-1)}{x\sqrt{{{x}^{2}}-1}} \right)dx={{e}^{x}}\cos e{{c}^{-1}}x+C}\]You need to login to perform this action.
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