MathematicsRead the following passage carefully:If f(x) is a differentiable function, then ∫exf(x)+f′(x)dx=exf(x)+c Using the above information. Simplify the following.If x∈0,π2, then ∫e−x/2⋅1−Sin⁡x1+Cos⁡xdx=

Read the following passage carefully:

If f(x) is a differentiable function, then exf(x)+f(x)dx=exf(x)+c 

Using the above information. Simplify the following.

If x0,π2, then ex/21Sinx1+Cosxdx=

  1. A

    ex/2Secx+c

  2. B

    ex/2Secx2+c

  3. C

    ex/2Secx2+c

  4. D

    ex/2Secx2+c

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    Solution:

    G.I=±ex/2sinx2cosx22cos2x2dx=±ex212secx2+12secx2tanx2dx=±ex2secx2

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