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Question Number 212341 by Spillover last updated on 10/Oct/24

Answered by Ghisom last updated on 10/Oct/24

$$\underset{0}{\stackrel{\pi /4}{\int }}\frac{\sin x+\cos x}{9+16\sin 2x}dx=$$$$[t=\frac{4\sqrt{2}}{5}\cos (x+\frac{\pi }{4})]$$$$=-\frac{1}{20}\underset{0}{\stackrel{4/5}{\int }}\frac{dt}{t^2-1}=-\frac{1}{40}{[\ln \mid \frac{t-1}{t+1}\mid ]}_{}=\frac{\ln 3}{20}$$

Commented by Spillover last updated on 12/Oct/24

$$great$$

Answered by MathematicalUser2357 last updated on 13/Oct/24

$$5.49306144335\times {10}^{-2}$$

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