What is the value of the definite integral of x^2/(x^3+1)^2 from x = 1 to x = 2?
Let f(x) = x^2/(x^3+1)^2
We need to find the integral of f(x) from 1 to 2.
Let F(x) = Int f(x)
==> The definite integral is:
I = F(2) = F(1).
Let us determine F(x).
==> F(x) = Int = x^2/(x^3+1)^2 dx
Let us assume that x^3+1 = u ==> du 3x^2 dx
==> F(x) = Int (1/u^2) * du/3
= Int du/ 3u^2
= (1/3) Int u^-2 du = (1/3) u^-1/-1...
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