Bài tập: Tính \( I = \int \frac{x}{3x - \sqrt{9x^2 - 1}} \, dx \)

A. \( I = \frac{1}{27} \left( 9x^2 + 1 \right)^{\frac{3}{2}} + x^3 + C \) 

B. \( I = \frac{1}{27} \left( 9x^2 - 1 \right)^{\frac{3}{2}} + \frac{x^3}{3} + C \) 

C. \( I = \frac{1}{27} \left( 9x^2 - 1 \right)^{\frac{3}{2}} + x^3 + C \) 

D. \( I = \frac{1}{54} \left( 9x^2 - 1 \right)^{\frac{3}{2}} + x^3 + C \)  

\( \int \frac{\cos x - \sin x}{1 + \sin 2x} \, dx \)

\( \int \frac{\cos 2x}{(\sin x + \cos x + 2)^2} \, dx \)

\( \int \left( \frac{\sin x - \cos x}{\sin x + \cos x} \right)^2 \, dx \)

\( \int \left( \frac{\sin x - \cos x}{\sin x + \cos x} \right)^3 \, dx \)

\( \int \frac{\ln(e x)}{3 + x \ln x} \, dx \)     (HVQHQT.96)

\( \int \frac{(1+x)e^x}{1 + x e^x} \, dx \quad\)(SGK chuẩn})