Nguyên hàm 3

Tính nguyên hàm $I=\displaystyle\int\dfrac{\sin x+\cos x}{(e^x \sin x+1)\sin x}dx$

$$\begin{aligned}I&=\int\frac{(\sin x+\cos x)e^x}{(e^x \sin x+1)e^x\sin x}dx\\ &=\int\frac{d(e^x\sin x)}{(e^x\sin x+1)e^x\sin x}\\ &=\int\frac{d(e^x\sin x)}{e^x\sin x}-\int\frac{d(e^x\sin x)}{e^x\sin x+1}\\ &=\ln\frac{e^x\sin x}{e^x\sin x+1}+C \end{aligned}$$