Let
F=∫14x2+x+12x+1dx.
Answer the following, giving exact values unless instructed otherwise.
(1) Evaluate F analytically, showing each step of your calculation.
(2) State your final answer in terms of a natural logarithm and simplify as far as possible.
(3) Without using a calculator, decide whether F is positive or negative. Justify your conclusion by referencing properties of the natural logarithm or the integrand, as appropriate.