5 ways: integral ∫a^(px+q) dx

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

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 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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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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trig integral a) Show that sin(t) cos(t)=1/2 sin^2(t)+c

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trig integral a) Show that sin(t) cos(t)=1/2 sin^2(t)+c

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

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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

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2nd way: integral ∫ log √x(x^n) dx

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2nd way: integral ∫ log √x(x^n) dx

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

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

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

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

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derivative log f(g(x)) (p(r(x)))

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derivative log f(g(x)) (p(r(x)))

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

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

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Cancellation Law ❌ Matrices

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Cancellation Law ❌ Matrices

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2 ways: Σ 1? where k=m to n

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2 ways: Σ 1? where k=m to n

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1st/2parts: Linear interpolation (2 given points)

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1st/2parts: Linear interpolation (2 given points)

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Let f(x,y)=4-2xx^2-y^2. Find the slope of the tangent line at the point (1,1,1) on the curve formed

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Let f(x,y)=4-2xx^2-y^2. Find the slope of the tangent line at the point (1,1,1) on the curve formed

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Variance measured in the squares of the units for the observations.

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Variance measured in the squares of the units for the observations.

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exp integral ∫(1+e^x)/(1-e^x) dx

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exp integral ∫(1+e^x)/(1-e^x) dx

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If x=at^2,, y=2at, then find d2y/dx2

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If x=at^2,, y=2at, then find d2y/dx2

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

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

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