How to evaluate $$\int \frac{\cos^{2}x-\sin x}{\cos x\left ( 1+\cos xe^{\sin x} \right )}dx$$ I don't know where to start.A little help will be great.
2026-04-07 02:22:52.1775528572
Evaluate $\int \frac{\cos^{2}x-\sin x}{\cos x\left ( 1+\cos xe^{\sin x} \right )}dx$
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Hint: $$\int \frac{\cos^{2}x-\sin x}{\cos x\left ( 1+\cos xe^{\sin x} \right )}\, \mathrm{d}x=\int \frac{e^{\sin x}\left (\cos^{2}x-\sin x \right )}{\cos xe^{\sin x}\left ( 1+\cos xe^{\sin x} \right )}\, \mathrm{d}x=\int \frac{\mathrm{d}\left ( \cos xe^{\sin x} \right )}{\cos xe^{\sin x}\left ( 1+\cos xe^{\sin x} \right )}$$ Then you can take it from here.