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Question Number 183794 by cortano1 last updated on 30/Dec/22

$$If\underset{0}{\stackrel{\pi }{\int }}\frac{\cos x}{{(x+2)}^2}dx=T$$$$then\underset{0}{\stackrel{\pi }{\int }}\frac{\sin 2x}{x+1}dx=?$$

Commented by Frix last updated on 30/Dec/22

$$\int \frac{\cos x}{{(x+2)}^2}dx=\sin 2\mathrm{Ci}(x+2)-\cos 2\mathrm{Si}(x+2)-\frac{\cos x}{x+2}+C_1$$$$\int \frac{\sin 2x}{x+1}dx=\cos 2\mathrm{Si}(2x+2)-\sin 2\mathrm{Ci}(2x+2)+C_2$$$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{see}\mathrm{any}\mathrm{connection},\mathrm{blame}\mathrm{it}\mathrm{on}\mathrm{me}...$$$$\mathrm{But}\mathrm{are}\mathrm{you}\mathrm{sure}{\mathrm{there}}^{\prime }\mathrm{s}\mathrm{no}\mathrm{typo}\mathrm{in}\mathrm{your}\mathrm{question}?$$

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