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Integrate the function
$\frac{\sin x}{1+\cos x}$
$\frac{\sin x}{1+\cos x}$
Solution:
2825 Upvotes
Verified Answer
Put $1+\cos x=t \Rightarrow-\sin x d x=d t$
$\begin{aligned}
&\therefore \int \frac{\sin x}{1+\cos x} d x=\int-\frac{d t}{t}=-\log t+\mathrm{C} \\
&=-\log (1+\cos x)+\mathrm{C}
\end{aligned}$
$\begin{aligned}
&\therefore \int \frac{\sin x}{1+\cos x} d x=\int-\frac{d t}{t}=-\log t+\mathrm{C} \\
&=-\log (1+\cos x)+\mathrm{C}
\end{aligned}$
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