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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")