Let $\mathrm{f}(x)=\int \frac{x^2-3 x+2}{x^4+1} \mathrm{~d} x$, then function decreases in the interval

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{f}(x)=\int \frac{x^2-3 x+2}{x^4+1} \mathrm{~d} x \ & \Rightarrow \mathrm{f}^{\prime}(x)=\frac{x^2-3 x+2}{x^4+1} \end{aligned}$ For $\mathrm{f}(x)$ to be decreasing, $\begin{aligned} & \mathrm{f}^{\prime}(x) < 0 \ & \Rightarrow \frac{x^2-3 x+2}{x^4+1} < 0 \ & \Rightarrow \frac{(x-1)(x-2)}{x^4+1} < 0 \ & \Rightarrow(x-1)(x-2) < 0 \ & \Rightarrow x \in(1,2) \end{aligned}$

Let $\mathrm{f}(x)=\int \frac{x^2-3 x+2}{x^4+1} \mathrm{~d} x$, then function decreases in the interval

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