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

2024 CMIMC Integration Bee, 2
Tags: integration bee , calculus , integration
\[\int_0^2 |\sin(\pi x)|+|\cos(\pi x)|\mathrm dx\] [i]Proposed by Anagh Sangavarapu[/i]

2021 CMIMC Integration Bee, 3
Tags: CMIMC , integration bee
$$\int_{0}^{\frac{\pi}{2}}\sin^2(x)\sin(2x)\,dx$$ [i]Proposed by Connor Gordon[/i]

2022 CMIMC Integration Bee, 5
Tags: calculus , integration , integration bee
\[\int \frac{1}{(1+x)\sqrt{x}}\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 8
Tags: calculus , integration , integration bee
\[\int_{-10}^{10}|4-|3-|2-|1-|x|||||\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 6
Tags: calculus , integration , integration bee
\[\int_0^2 e^x(x^4+8x^3+18x^2+16x+5)\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2024 CMIMC Integration Bee, 4
Tags: integration bee , calculus , integration
\[\int_0^1 (x^6+6x^5+15x^4+15x^2+6x+1)\mathrm dx\] [i]Proposed by Robert Trosten[/i]

2024 CMIMC Integration Bee, 3
Tags: calculus , integration , integration bee
\[\int_0^1 \frac{\log(x)}{\sqrt x}\mathrm dx\] [i]Proposed by Robert Trosten[/i]

2021 CMIMC Integration Bee, 15
Tags: calculus , integration , CMIMC , integration bee
$$\int_{-\infty}^\infty \frac{\sin(\pi x)}{x(1+x^2)}\,dx$$ [i]Proposed by Vlad Oleksenko[/i]

2021 CMIMC Integration Bee, 7
Tags: calculus , integration , CMIMC , integration bee
$$\int_0^\infty \frac{1}{(x^2+4)^{5/2}}\,dx$$ [i]Proposed by Connor Gordon[/i]

2022 CMIMC Integration Bee, 2
Tags: integration bee
\[\int_{-2}^2 |1-x^2|\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 10
Tags: calculus , integration , integration bee
\[\int_{\frac 1{\sqrt 3}}^{\sqrt 3} \frac{\arctan(x)\log^2(x)}{x}\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2024 CMIMC Integration Bee, 12
Tags: calculus , integration , integration bee
\[\int_1^\infty \frac{\sec^{-1}(x^{2})-\sec^{-1}(\sqrt x)}{x\log(x)}\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 12
Tags: calculus , integration , integration bee
\[\lim_{n\to\infty} n^2 \int_0^1 x^n e^{-x}\log(x)\,\mathrm dx\] [i]Proposed by Connor Gordon and Vlad Oleksenko[/i]

2022 CMIMC Integration Bee, 9
Tags: calculus , integration , integration bee
\[\int_e^{e^2} (\log(x))^{\log(x)}(2+\log(\log(x)))\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 1
Tags: integration bee , calculus , integration
\[\int_2^0 x^2+3\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2023 CMIMC Integration Bee, 15
Tags: calculus , integration , integration bee
\[\int_0^\infty \left(1-e^{-\pi/x^2}\right)^2\,\mathrm dx\] [i]Proposed by Vlad Oleksenko[/i]

2023 CMIMC Integration Bee, 4
Tags: calculus , integration , integration bee
\[\int_0^\infty x e^{-\sqrt[3]{x}}\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2024 CMIMC Integration Bee, 13
Tags: calculus , integration , integration bee
\[\int_0^{2\pi} \frac{1}{3+2 \sqrt{3} \cos x + \cos^2 x}\mathrm dx\] [i]Proposed by Robert Trosten[/i]

2024 CMIMC Integration Bee, 15
Tags: calculus , integration , integration bee
\[\int_0^\infty 1+\cos\left(\tfrac 1{\sqrt x}\right)-2\cos\left(\tfrac 1{\sqrt {2x}}\right)\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2021 CMIMC Integration Bee, 9
Tags: calculus , integration , CMIMC , integration bee
$$\int_1^2\frac{12x^3+12x+12}{2x^4+3x^2+4x}\,dx$$ [i]Proposed by Connor Gordon[/i]

2021 CMIMC Integration Bee, 1
Tags: calculus , integration , CMIMC , integration bee
$$\int_0^5 \max(2x,x^2)\,dx$$ [i]Proposed by Connor Gordon[/i]

2021 CMIMC Integration Bee, 14
Tags: CMIMC , integration bee
$$\int_0^\infty \frac{\sin(20x)\sin(21x)}{x^2}\,dx$$ [i]Proposed by Connor Gordon and Vlad Oleksenko[/i]

2021 CMIMC Integration Bee, 8
Tags: calculus , integration , CMIMC , integration bee
$$\int\left(\frac{x-1}{x^2+1}\right)^2e^x\,dx$$ [i]Proposed by Connor Gordon[/i]

2022 CMIMC Integration Bee, 8
Tags: calculus , integration , integration bee
\[\int_{-\infty}^{0} \frac{1}{e^{-x}+2e^{x}+e^{3x}}\,\mathrm dx\] [i]Proposed by Connor Gordon[/i]

2021 CMIMC Integration Bee, 13
Tags: calculus , integration , CMIMC , integration bee
$$\int_0^1 x\ln(x^2)\ln(1+x)\,dx$$ [i]Proposed by Connor Gordon[/i]