If $\int \frac{2x - 5}{(2x - 3)^3} e^{2x} dx = \frac{\lambda e^{2x}}{(2x - 3)^2} + C$, where $C$ is an arbitrary constant then the value of $\lambda$ is

For $x \in \left(0, \frac{\pi}{2}\right)$, $\int \frac{\sin x + \cos x}{\sqrt{\sin 2x}} dx$ is equal to

$I=\int(\log x)^2dx$ is equal to :(Consider $\log_e x=\log x$)

$\int_0^{\pi/2} \frac{\sin^8 x}{\sin^8 x + \cos^8 x} dx$ is equal to

Match List I with List II

$\int \frac{x}{(x^2+3)(x^2+4)} dx =$

$\int\frac{\tan^5\sqrt{x}.\sec^2\sqrt{x}}{\sqrt{x}}dx$ is equal to: