Web Reference: Mar 23, 2026 · Encountering the integral $$ \\int \\frac{x^2-2}{\\left(x^2+2\\right) \\sqrt{x^4+4}} d x, $$ from MIT integration 2026 Semifinal , I tried my best to finish it within the time limit. $$ \\begin{aligned} ... The integral which you describe has no closed form which is to say that it cannot be expressed in elementary functions. For example, you can express $\int x^2 \mathrm {d}x$ in elementary functions such as $\frac {x^3} {3} +C$. Answers to the question of the integral of $\frac {1} {x}$ are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers.
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