sssgggg2827 sssgggg2827
  • 02-12-2017
  • Mathematics
contestada

Find a formula for the function f(x) such that f′(x)=(ln(x))^2/x and f(2)=6

Respuesta :

chudung1976
chudung1976 chudung1976
  • 02-12-2017
f(x)= ∫ln²x/x dx= ∫ln²xd(lnx) cause d(lnx)= (lnx)'dx=1/x dx
= ln³x/3 +C with C is constant
In addition, we have f(2)=6, so we have 6=ln³2/3+C
or C= 6- ln³2/3
And f(x)= 
ln³x/3+  6- ln³2/3
Answer Link

Otras preguntas

-k(-4k^2+k+2) Best one and simplest one gets the brainliest, I'm In a rush.
What is the value of y? 4 2 10 5
Please answer this correctly
Please associate the indirect object pronoun in column A to the sentences in column B.
Convert 1/6 to a percent
Find the length and midpoint of the segment with the given endpoints (-7,-10,9), (-2,9,-9)
Product of two numbers is -216. If one of the number is 12, find the other number
How to have self confidence when your really shy
What is -x+y +2x+y ?
A, B and C are collinear and B is between a and C. The ratio of AB to AC is 3:2. If A is at (4,8) and B is at (7,2) what are the coordinates of point C