The value of $\displaystyle\int_{\pi/6}^{\pi/3} \dfrac{\sin x+\cos x}{\sqrt{\sin 2x}}\,dx$ is:

$\int \sin x \sin 2x \sin 3x dx$ is equal to

$\displaystyle\int \dfrac{x + \dfrac{a}{x}}{x^2 + \dfrac{a^2}{x^2}}\,dx, a > 0$ is equal to (where C is an arbitrary constant)

$\int \frac{(x^4 - x)^{1/4}}{x^5} dx$ is equal to

Match List-I with List-II

Choose the correct answer from the options given below:

$\int \frac{x}{(x-1)(x-2)} dx =$

(where c is an arbitrary constant)

$\displaystyle\int \dfrac{1+\cos\theta}{1-\cos\theta}\,d\theta =$