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

2nd/2 parts: 2 (elementary) rules

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integral ∫ x dx withOUT using Power rule.

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

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

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

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

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2nd way: integral ∫ log √x(x^n) dx

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2nd way: trig integral ∫1/(sin(x) cos(x)) dx

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#5 MIT 2022 Integration Bee Qualifying Exam

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1st/2parts: 2 (elementary) rules

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2nd way: Evaluate ∫a/(b+ce^x)dx

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2nd way: trig integral ∫sin^6(ax+b) cos^6(ax+b) dx

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2nd way: Express as partial fractions

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Solve √(2x-5) -√(x-2) = 2

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

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Determine the equation of the normal drawn to the astroid ...

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#16 MIT 2022 Integration Bee Qualifying Exam

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Alternate way: integral ∫ax+b dx

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