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

Which options could be the next step in simplifying this expression? (18 + 23) + 7 Choose exactly two answers that are correct. A. 18 + 30
What is 1600 divided by 70?
Why did the North industrialize faster than the South? A. The Northern workers had a better work ethic. B. Southern climate made it difficult to operate facto
muscle cells would contain a high number of
Karleigh walks 5/8 mile to school every day. How far does she walk to school in 5 days?
How can you argue that imperialism was more important than alliances and militarism as the underlying cause of World War I?
What is the sum? 10/19+3/19
What did Bohr’s model of the atom include that Rutherford’s model did not have?
why do the sun and the moon appear to move across the sky each day
Who became king of France after Napoleon was exiled? Louis XVIII Georges Danton Joseph Guillotin Joseph Bonaparte