derivative If y=acos(log(x)) + bsin(log(x)), prove that x^2y2+xy1+y=0

UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

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2nd way: integral ∫ log √x(x^n) dx

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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logic Idempotent law show x=xVx

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

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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

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#4 2017 MIT Integration Bee Qualifying Exam

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2nd way: sqrt trig integral ∫1/(√x cos^2(√x)) dx

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Add math: Find the equation of the line ...

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UC Davis #3 2nd way: ∫(2-x)/(x^2+5x)dx [integration by partial fraction]

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2nd way: trig integral ∫1/(1+sec(x)) dx

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Hurry Up and Call Me Dad

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

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Find the number of permutations of the letters of the word ALLAHABAD

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MPPET 1993 BIT Ranchi 1982 Hindusta: trig integral ∫ (1+cos^2(x)/sin^2(x) dx

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prob stat: The following frequency table gives the values obtained

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