To evaluate the integral [tex]\(\int_1^3 6 f(x) \, dx\)[/tex], we can use the property of integrals that allows us to factor out a constant. This property states that for any constant [tex]\(c\)[/tex],
[tex]\[ \int_a^b c \cdot f(x) \, dx = c \cdot \int_a^b f(x) \, dx. \][/tex]
Given the integral [tex]\(\int_1^3 f(x) \, dx = 5\)[/tex], we will apply this property with [tex]\(c = 6\)[/tex]:
[tex]\[ \int_1^3 6 f(x) \, dx = 6 \cdot \int_1^3 f(x) \, dx. \][/tex]
Substituting the given value of [tex]\(\int_1^3 f(x) \, dx\)[/tex]:
[tex]\[ \int_1^3 6 f(x) \, dx = 6 \cdot 5. \][/tex]
Thus,
[tex]\[ \int_1^3 6 f(x) \, dx = 30. \][/tex]
Therefore, the answer is [tex]\(30\)[/tex].
