This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 59

2022 CMIMC Integration Bee, 13
Tags: calculus , integration , integration bee
\[\int_{-\infty}^\infty e^{-x^2-4/x^2}\,\mathrm dx\] [i]Proposed by Vlad Oleksenko[/i]

2022 CMIMC Integration Bee, 11
Tags: calculus , integration , integration bee
\[\int_0^{\pi/2} \frac{\sin(x)}{2-\sin(x)\cos(x)}\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 11
Tags: calculus , integration , integration bee
\[\int_{-1}^1 \frac{1}{(8 + x^2)\sqrt{1-x^2}} \,\mathrm dx\] [i]Proposed by Vlad Oleksenko[/i]

2022 CMIMC Integration Bee, 3
Tags: calculus , integration , integration bee
\[\int_0^1 x\sqrt[4]{1-x}\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 7
Tags: calculus , integration , integration bee
\[\int_0^{\frac \pi 2} \left(\frac{1}{1-\cos(x)}-\frac{2}{x^2}\right)\,\mathrm dx\] [i]Proposed by Vlad Oleksenko[/i]

2023 CMIMC Integration Bee, 9
Tags: calculus , integration , integration bee
\[\int_{-1}^1 x^{2022}\cos\left(\tfrac \pi {12}-x\right)\sin\left(\tfrac \pi{12}+x\right)\,\mathrm dx\] [i]Proposed by Michael Duncan, Connor Gordon, and Vlad Oleksenko[/i]

2022 CMIMC Integration Bee, 4
Tags: calculus , integration , integration bee
\[\int_0^1 \sqrt{x}\log(x)\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 13
Tags: calculus , integration , integration bee
\[\int_0^1 2^{\sqrt x}\log^2(2)+\log^2(1+x)\,\mathrm dx\] [i]Proposed by Thomas Lam[/i]

2024 CMIMC Integration Bee, 11
Tags: calculus , integration bee , integration
\[\int_1^\infty \frac{\lfloor x^2\rfloor}{x^5}\mathrm dx\] [i]Proposed by Robert Trosten[/i]

2024 CMIMC Integration Bee, 14
Tags: calculus , integration , integration bee
\[\int_1^\infty \frac{\lfloor x \rfloor}{9x^3-x}\mathrm dx\] [i]Proposed by Robert Trosten and Connor Gordon[/i]

2024 CMIMC Integration Bee, 6
Tags: calculus , integration , integration bee
\[\int_1^2 \frac{\sqrt{1-\frac 1x}}{x^2-1}\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2022 CMIMC Integration Bee, 10
Tags: calculus , integration , integration bee
\[\int_0^1 \frac{(x+1)\log(x)}{x^3-1}\,\mathrm dx\] [i]Proposed by Vlad Oleksenko[/i]

2022 CMIMC Integration Bee, 15
Tags: calculus , integration , integration bee
\[\int_0^\infty 1+\frac{2}{\sqrt[x]{8}}-\frac{3}{\sqrt[x]{4}}\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 3
Tags: calculus , integration , integration bee
\[\int_0^{\frac \pi 4} \cot(x)\sqrt{\sin(x)}\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2024 CMIMC Integration Bee, 7
Tags: integration bee , calculus , integration
\[\int_1^2 \frac{\sqrt{1-\frac 1x}}{x-1}\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2024 CMIMC Integration Bee, 1
Tags: integration bee , calculus , integration
\[\int_1^e \frac{\log(x^{2024})}{x} \mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 2
Tags: calculus , integration , integration bee
\[\int_0^1 \frac{1}{x+\sqrt x}\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2021 CMIMC Integration Bee, 2
Tags: CMIMC , integration bee
$$\int\frac{\ln^2(x)}{x}\,dx$$ [i]Proposed by Connor Gordon[/i]

2024 CMIMC Integration Bee, 8
Tags: calculus , integration , integration bee
\[\int_1^2 \cos(\sin^{-1}(\tan(\cos^{-1}(\sin(\tan^{-1}(x))))))\mathrm dx\] [i]Proposed by Robert Trosten[/i]

2022 CMIMC Integration Bee, 1
Tags: integration bee , calculus , integration
\[\int_0^{\pi/1011}\sin^2(2022x)+\cos^2(2022x)\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 14
Tags: calculus , integration , integration bee
\[\int_0^\infty e^{-\lfloor x \rfloor(1+\{x\})}\,\mathrm dx\] [i]Proposed by Vlad Oleksenko[/i]

2022 CMIMC Integration Bee, 14
Tags: calculus , integration , integration bee
\[\int_2^\infty \frac{\pi(x)}{x^3 - x}\,dx\] [i]Proposed by Vlad Oleksenko[/i]

2022 CMIMC Integration Bee, 6
Tags: calculus , integration , integration bee
\[\int_0^{2022} \{x\lfloor x \rfloor\}\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2021 CMIMC Integration Bee, 6
Tags: calculus , integration , CMIMC , integration bee
$$\int_0^{20\pi}|x\sin(x)|\,dx$$ [i]Proposed by Connor Gordon[/i]

2022 CMIMC Integration Bee, 7
Tags: calculus , integration , integration bee
\[\int_{-1}^1 \sqrt{\frac{1+x}{1-x}}+\sqrt{\frac{1-x}{1+x}}\,\mathrm dx\] [i]Proposed by Vlad Oleksenko[/i]