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alternate way: ∫ √(x^2+a^2 )dx via "expressing in 2 ways"
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logic: tautology (¬p→q)∧(¬p→¬q) →p
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🪔 Happy Deepavali 🪔 [Nov-12-2023]
A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...
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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)
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2010 #2 MIT Integration Bee
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2 ways: exp log integral ∫3^(log81(x)) dx
Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction
JHU: integral ∫t^3 e^(t^2) dt
#17 2022 MIT Integration Bee Qualifying Exam
Conversion: Permutation - Combination vice versa
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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt
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#16 2014 MIT Integration Bee Qualifying Exam
integral ∫(8x+12) (x^2+3x+1)^4 dx vs integral ∫(8x+12)/(x^2+3x+1)^4
#1 2019 MIT Integration Bee Final
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AP Calculus integral 1)∫√x dx vs 2) ∫√(x-a) dx
#17 2012 MIT Integration Bee Qualifying Exam
Screen Recording 2024-03-03 at 12.00.11 AM
exp integral ∫ a^x da
West Virginia U: exp integral ∫3^x (2^x)^3/((6^x 4^(2x)) dx