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4th way: rational function integral ∫x^3/√ (1+x^2) dx

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KITE MY LOVE

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

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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319

KITE MY LOVE

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JEE Main integral x^2/(a+bx)^2 dx

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Careful: arc sin(sin(5π/4)) ≠ ...

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2 ways: Show logb^n(a)=1/n logb(a)

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logic: Show p→q ≡¬ p∨q

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Alternate way: trig integral ∫sec(x) dx= ln(tan(/π4+x/2)) + c

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trig integral ∫tan^n(x) dx where n is EVEN via Reduction formula

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#8 2020 MIT Integration Bee Quali Exam: integral ∫x/(1-x^4) dx

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commutative: ab=ba via "picture"

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#3 2024 MIT Integration Bee Qualifying Exam

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logic: Simplify the Boolean function F=XYZ+XY'Z+XYZ'

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Jisan Haque_7300

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2nd/2ways: [k map] logic Simplify the Boolean function F=AB+BC+B'C

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2 ways: trig integral ∫1/(2+cos^2(x)) dx

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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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1st/2 way: Expand e^sin(x) by Maclaurin's Theorem

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Laman utama>4th way: rational function integral ∫x^3/√ (1+x^2) dx>