2 ways: log derivative y=ln(a+b)

“The Dead Last in the Zen Temple Family”

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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Pantun Melayu [Sorong papan tarik papan]

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trig Write each expression as an equivalent algebraic expression involving only x.

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

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

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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

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NONelementary integral ∫e^(ax)/x dx

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trig Evaluate each expression below withOUT using a calculator.

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examples: 2x2 matrix which is its own inverse

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integral ∫√(x-a)/x dx

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Always ZERO

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What is π?

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3rd/3ways: trig integral ∫sec(x) dx

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2 ways: integral ∫x/(x+a) dx

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Alternate way: trig integral ∫cos(x) dx

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log derivative ln(x) via chain rule

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2nd Alt. way: log Taylor series of ln(sec(x)) withOUT Taylor series explicitly

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

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