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Question Number 88045 by jagoll last updated on 08/Apr/20

$$\int \frac{\sin \mathrm{x}}{2\sin \mathrm{x}+\cos \mathrm{x}}\mathrm{dx}$$

Commented by john santu last updated on 08/Apr/20

$$\frac{\sin \mathrm{x}}{2\sin \mathrm{x}+\cos \mathrm{x}}=\frac{2}{5}-\frac{1}{5}\left[\frac{2\cos \mathrm{x}-\sin \mathrm{x}}{2\sin \mathrm{x}+\cos \mathrm{x}}\right]$$$$\Rightarrow \int \{\frac{2}{5}-\frac{1}{5}\left[\frac{2\cos \mathrm{x}-\sin \mathrm{x}}{2\sin \mathrm{x}+\cos \mathrm{x}}\right]\}\mathrm{dx}$$$$=\frac{2\mathrm{x}}{5}-\frac{1}{5}\log \mid 2\sin \mathrm{x}+\cos \mathrm{x}\mid +\mathrm{c}$$

Commented by jagoll last updated on 08/Apr/20

$$\mathrm{waw}...\mathrm{super}\mathrm{easy}$$

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