Evaluate ∫$$ex1$$−$$sin$$⁡$$x1$$−$$cos$$⁡xdx

Correct option is 2−excot⁡x2+c

Questions

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

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excot⁡x2+c

−excot⁡x2+c

−excot⁡x+c

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detailed solution

Correct option is B

=∫ex1−sin⁡x1−cos⁡xdx=∫ex1−2sin⁡x2cos⁡x22sin2⁡x2dx=∫ex12cosec2⁡x2−cot⁡x2dx=−∫excot⁡x2+cot⁡x2′dx using the formula ∫exf(x)+f′(x)dx=exf(x)+C=−excot⁡x2+c

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Evaluate ∫ex1−sin⁡x1−cos⁡xdx

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