alternate way: count sum 1+3+5+ ... +(2n-1)

If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0

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integral ∫ x dx withOUT using Power rule.

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(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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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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2nd way: integral ∫ log √x(x^n) dx

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log sq root integral ∫ln(√ x^3)/√ √ x dx

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Cancellation Law ❌ Matrices

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integral ∫logb(√x) dx

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UC Davis: 4 ways exp integral ∫7^(2x+3) dx

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3rd/3 ways: trig integral ∫ sin(ax+b) dx

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Solve cos^2(x) dy/dx +y = tan(x) via Integrating factor[IF]

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1st/3 ways: Show 1+2+3+...+n=n(1+n)/2 via picture

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#5 MIT 2022 Integration Bee Qualifying Exam

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logic: tautology p→q≡(¬q→¬p)

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Alternate way: Evaluate exp integral ∫1/√(1-e^(2x)) dx

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UC Davis #14: integral ∫x √(4-x) dx

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