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# I have to calculate [0,1] (x^3-x^5)/log(x) dx.
f = function(x) (x^3-x^5)/log(x)
# In 0 and 1 f is not defined. But if I make the graph:
BF=3; HF=2.8
graphF( f,0,1, "brown")
# I obtain the graph below on the left:
                         
# After all:
f(0); f(1)
# 0   NaN     as x -> 1 f(x) -> -2, indeed:
f(1-1e-10)
# -2
# I could extend f like this:  f(0)=1  f(1)=-2
# Dunque  [0,1] (x^3-x^5)/log(x) dx  must be a negative number.
# From the graph I understand it is near -1/2. We perform the calculation:
integral(f, 0,1)
# -0.4054651
# Is it the logarithm of something?
exp(integral(f, 0,1))
# 0.6666667
fraction(exp(integral(f, 0,1)))
# 2/3
log(2/3)
# -0.4054651
# I can draw the graph of the "integral function" x -> [0,x] f (the graph IF above):
Plane(0,1, 0,-0.5)
Gintegra(f, 0,1, "seagreen")
POINT(1,log(2/3),"red")