$\int_1^4 \frac{\{x\}}{[x]} dx$ is equal to

[Where $\{x\}$ = fractional part function and $[x]$ = greatest integer function]

The value of $\int_{\pi/2}^{\pi} \frac{1}{1 + \cot x} dx$ is equal to:

The value of $\int_{0}^{1} \frac{e^x}{1+e^{2x}}\,dx$ is

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

Match the LIST-I with LIST-II (where $[x]$ denotes greatest integer function)

Choose the correct answer from the options given below:

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

In which of the following cases the value of the integral is more than 10?

A. $\displaystyle\int_0^2 |x|\,dx$

B. $\displaystyle\int_0^2 (x+3)^2\,dx$

C. $\displaystyle\int_0^2 e^x\,dx$

D. $\displaystyle\int_0^2 (2x+5)\,dx$

Choose the correct answer from the options given below: