Questions

$\int \frac{(e^{x} + e^{- x}) + (e^{x} - e^{- x}) \sin x}{1 + \cos x} d x =$

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ex+e−xtan⁡(x/2)+C

ex−e−xcot⁡(x/2)+C

ex−e−xsec⁡(x/2)+C

ex−e−xcosec⁡(x/2)+C

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detailed solution

Correct option is A

I=∫ex+e−x+ex−e−xsin⁡x1+cos⁡xdx=∫ex+e−x1+cos⁡x+ex−e−xsin⁡x1+cos⁡xdx=∫ex+e−x12sec2⁡x2+ex−e−xtan⁡x2dx=∫ddxex+e−xtan⁡x2dx=ex+e−xtan⁡(x/2)+C

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