Question
Evaluate the following intregals:
$\int\frac{\text{x}^2+\text{x}+1}{(\text{x}+1)^2(\text{x}+2)}\ \text{dx}$
$\int\frac{\text{x}^2+\text{x}+1}{(\text{x}+1)^2(\text{x}+2)}\ \text{dx}$
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$\frac{1}{\sin x+\sin 2 x}$
$\tan ^{-1}\left[\frac{\cos \theta+\sin \theta}{\cos \theta-\sin \theta}\right]=\frac{\pi}{4}+\theta$ if $\theta \in\left(-\frac{\pi}{4}, \frac{\pi}{4}\right)$