Step 1: When sec-butylcyclohexane reacts with bromine in the presence of sunlight, a free radical substitution reaction occurs.
Step 2: In this reaction, the bromine atom will substitute one of the hydrogen atoms at the benzylic position of sec-butylcyclohexane. The benzylic hydrogen is the most reactive in this case due to the stability of the resulting free radical formed by the abstraction of the hydrogen atom.
Step 3: Therefore, the major product will have a bromine atom attached to the carbon atom adjacent to the cyclohexane ring, which is the sec-butyl position.
If \[ f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6 \], then f(1) is equal to: