Chapter 5, Problem 57RE

(a) Use differentiation to prove that the function

$F\left(x\right)={\displaystyle {\int }_0^x\frac{1}{1+t^2}dt}+{\displaystyle {\int }_0^{1/x}\frac{1}{1+t}dt}$

is constant on the interval $\left(0,+\infty \right)$ .

(b) Determine the constant value of the function in part (a) and then interpret (a) as an identity involving the inverse tangent function.