Answer
$${\text{FALSE}}$$
Work Step by Step
$$\eqalign{
& \int {\frac{{dx}}{{25 + {x^2}}}} \cr
& {\text{Rewrite the integrand}} \cr
& = \int {\frac{{dx}}{{{{\left( 5 \right)}^2} + {x^2}}}} \cr
& {\text{Integate by the formula }}\int {\frac{{du}}{{{a^2} + {x^2}}}} = \frac{1}{a}\arctan \left( {\frac{x}{a}} \right) + C \cr
& \int {\frac{{dx}}{{{{\left( 5 \right)}^2} + {x^2}}}} = \frac{1}{5}\arctan \left( {\frac{x}{5}} \right) + C \cr
& \frac{1}{5}\arctan \left( {\frac{x}{5}} \right) + C = \frac{1}{{25}}\arctan \left( {\frac{x}{{25}}} \right) + C \cr
& {\text{Therefore, the statement is FALSE}} \cr} $$
