(1 point) Write an expression for the function, f(x), with the properties. f′(x)=(ln(x)2)/x and f(3)=7.

Question

f(x)=∫t=b
t=a

Answer 1

f′(x)=ln^2(x)/x
let u=lnx and you have f'(x) = u^2 du
f(x) = 1/3 ln^3(x)+C
f(3)=7, so
1/3 ln^3(3)+C = 7
C = 7 - 1/3 ln^3(3)

f(x) = 1/3 ln^3(x) + 7 - 1/3 ln^3(3) ≈ 1/3 ln^3(x) + 6.558