# Solving integral $\int\frac{\sin x}{1+x\cos x}dx$

How I can find the anti-derivative? $$\int\frac{\sin x}{1+x\cos x}dx$$

• – user61527 Apr 16 '14 at 6:02
• Have you tried using the simplification of expressions option? – mahmoud afefey Apr 16 '14 at 6:16
• No. What is that? – Hamid Shafie Asl Apr 16 '14 at 6:16
• And where do you arrive ? – Claude Leibovici Apr 16 '14 at 7:11
• If no bounds, I am skeptical concerning the existence of a closed form solution. – Claude Leibovici Apr 16 '14 at 7:14

By using the formula http://upload.wikimedia.org/wikipedia/en/math/7/2/a/72a1058ad2087aec467af24bddcf9479.png, we have $\int\dfrac{\sin x}{1+x\cos x}dx=x\sum\limits_{n=1}^\infty\sum\limits_{m=1}^{2^n-1}\dfrac{(-1)^{m+1}\sin\dfrac{mx}{2^n}}{2^n+mx\cos\dfrac{mx}{2^n}}+C$