3 ways: trig integral ∫tan(x) sec^2(x) dx

integral ∫x^2/√(x^2+a^2) 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 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(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 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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trig integral ∫sin(x) cos(x) cos(2x) cos(4x) cos(8x) cos(16x) cos(32x) dx

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3 ways: sum Show 1+3+5+...nth term = n^2

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trig integral ∫1/(cos(x)(1+cos(x)) dx

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2nd way: integral ∫1/(a + √√b (x^2)) dx

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impIicit diff f x^y=y^x, find dy/dx at (2,4)

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logic: tautology p→q≡(¬q→¬p)

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exp integral ∫ (e^2x -1) /(e^2x +1)dx

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1st/2 ways: derivative y=(ln(x))^x

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2nd/10parts: Logical complement

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2nd/2ways: add math sum a + (a+d) + (a+2d) + ... + (a+(n-1)d) ?

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Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5

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Common log mistake: logb(xy^n) ≠ nlogb(xy)

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derivative differentiate x^sin(x) + (sin(x))^cos(x)

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