picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

1st way: exp ∫(e^x)/x (1+x log(x)) dx

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1st/3part: Maclaurin Series [ahp kia]

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Review: Linear form, Quadratic form & Bilinear form

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2nd way: integral ∫ log √x(x^n) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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1st/2ways: logic Import-Export

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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2nd way: integral ∫ 1/(5x^2 -3x +7) dx with BONUS

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Show log b^n(x^m) = m/n logb(x)

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3 ways: derivative a^(f(x)g(x))

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inverse trig Derivative arc sin(x)

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2nd/3part: Maclaurin Series [ahp kia]

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Calculus: Find nth derivative of sin(ax+b)

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4ways: exp trig integral ∫ e^(cos^2(x)) sin(2x) dx

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Pure Math: Calculate the coordinates of the two points on the curve

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#12 2024 MIT Integration Bee Qualifying Exam

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2nd/2parts: Linear interpolation (2 given points)

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2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1

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Matriculation & Calculus: Show if y=f(x) g(x) h(x) k(x)

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