What is $\int \frac{dx}{10^{x}+10^{-x}}$ equal to?

A wire of length 20 cm is to be bent into a rectangle. Which of the following statements is/are correct?

I. The rectangle of the largest area is the square.

II. It is possible to form a rectangle of an area of$ 27c m ^ 2$

Select the answer using the code given below.

If $I_{1}=\int _{e}^{e^{2}}\frac{dx}{ln~x}$ and  $I_{2}=\int _{1}^{2}\frac{e^{x}}{x}dx$  then which one of the following is correct?

What is the area of the region bounded by |x| <= 2k and |y| <= k where k is a positive real number?