sq root integral ∫1/ √(a^2-bx^2) dx

2 ways: integral ∫(x-a)/(x+a) dx

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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2nd way: integral ∫ log √x(x^n) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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2nd/3ways: trig integral ∫sec(x) dx

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Rintaro and Kaoruko - Episode 9

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examples: 2x2 matrix which is its own inverse

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Always ZERO

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Diff Eq: Solve sec(x) dy/dx=y+sin(x) via Integrating factor [IF]

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3rd/3ways: sum Show 1+2+3+...+n = n(1+n)/2

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Rintaro and Kaoruko - Episode 4

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1st/2ways: permutation Show P(n,2)+P(n,1)=n^2

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Rintaro and Kaoruko - Episode 7

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1st way: Differentiate the function w.r.t x log10(x)+logx(10)+logx(x)+log10(10)

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alternate way: count sum 1+2+3+ ... +n

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Rintaro and Kaoruko - Episode 5

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2 ways: diff eq Solve dy/dx=y-1

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1st/2 ways: derivative y=(ln(x))^x

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Rintaro and Kaoruko - Episode 8

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1st/2ways: add math sum a + (a+d) + (a+2d) + ... + (a+(n-1)d) ?

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