1st/3ways: derivative If f(x)=(x-a)(x-b)(x-c), show f'(x)/f(x)=1/(x-1)+1/(x-b)+1/(x-c)

If sec(x+y)=xy then find dy/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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Pantun Melayu [Sorong papan tarik papan]

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

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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

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

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Review: Linear form, Quadratic form & Bilinear form

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Penn. State U: Suppose the p.m.f of discrete random variable X is ...

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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trig integral a) ∫csc^2(x) dx

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2 ways: trig integral ∫tan(x)/sec^5(x) dx

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Alternate way: trig integral ∫sin(x) 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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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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STPM Math T Sem.2:

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2nd way: derivative x^n w.r.t x^x

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