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int(3x^2+2x)/(x^6+2x^5+x^4+2x^3+2x^2+5) ...

`int(3x^2+2x)/(x^6+2x^5+x^4+2x^3+2x^2+5) dx=F(x)` Fidn the value of `[F(1)-F(0)]` where [.] represents greatest integer function

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To solve the integral \( \int \frac{3x^2 + 2x}{x^6 + 2x^5 + x^4 + 2x^3 + 2x^2 + 5} \, dx = F(x) \) and find the value of \( [F(1) - F(0)] \), we will follow these steps: ### Step 1: Rewrite the integral We start with the integral: \[ \int \frac{3x^2 + 2x}{x^6 + 2x^5 + x^4 + 2x^3 + 2x^2 + 5} \, dx \] We can observe that the denominator can be rewritten. The polynomial in the denominator can be expressed as: ...
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