Methods of integration

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Question

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

Moderate

Solution

$\int [\frac{\cos x}{1 + \sin x} + \frac{- 1}{1 + \sin x}] e^{x} d x$
$\begin{array}{l} \int e^{x} [f (x) + f^{1} (x)] d x = e^{x} f (x) + c \\ f (x) = \frac{\cos x}{1 + \sin x} \end{array}$

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