What is the value of the definite integral of x^2/(x^3+1)^2 from x = 1 to x = 2?

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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...

(The entire section contains 2 answers and 198 words.)

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