I don't speak Romanian, but the closest translation for this suggests you're trying to compute
Integrate by parts:
where
u = ln(x)² ⇒ du = 2 ln(x)/x dx
dv = x³ dx ⇒ v = 1/4 x⁴
Integrate by parts again:
where
u' = ln(x) ⇒ du' = dx/x
dv' = x³ dx ⇒ v' = 1/4 x⁴
So, we have
Answer:
The complete question is as shown in the attached figure 1
The Venn diagram is the attached figure 2
Let: R⇒ribs , H⇒hamburgers and C⇒corn
People would eat all three = 53
People would eat only R and H = 56 - 53 = 3
People would eat only C and H = 54 - 53 = 1
People would eat only R and C = 55 - 53 = 2
People would eat only H = 60 - (53+3+1) = 60 - 57 = 3
People would eat only R = 59 - (53+3+2) = 59 - 58 = 1
People would eat only C = 56 - (53+1+2) = 0
See Vinn diagram.
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a. How many people did not want any of these foods?
people did not want any of these foods = 64 - (53+3+1+2+3+1) = 1
b. How many people would eat ribs but not corn?
people would eat ribs but not corn = 1+3 = 4
c. How many people would eat something as long as it was not a hamburger?
people would eat something as long as it was not a hamburger= 1+2 = 3
d. How many people would eat only corn?
people would eat only corn = 0
e. How many people would eat exactly two foods?
people would eat exactly two foods = 1 + 2 + 1
