2 ways: trig show tan(2x)=2tan(x)/1-tan^2(x))

UT Austin: integral ∫(1+sin^(x-1)) sin(x-1) cos(x-1) 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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2nd way: integral ∫ log √x(x^n) dx

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

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

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logic: If p then q ...

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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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Example: Find the sum

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2 ways: Find ∫(ax^x+bx+c) dx

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2 ways: integral ∫x/(x+a) dx

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count: How many subsets does {23,24,25,...,118} have?

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SALAH SATU HAL UNIK KATAKURI | TEKNIK SERANGANNYA MIRIP LUFFY?

Maddnime

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UC Davis: 4 ways exp integral ∫7^(2x+3) dx

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alternate way: count sum 1+2+3+ ... +n

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1st/2ways: exp e^g(x) (g'(x)f(x) + f'(x)) dx

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UT Austin: sq root integral ∫1/((√x) (1+ √x))dx

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trig integral ∫7x sin(x^2) sin(4x^2) dx

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Princeton U: Compute the integral ∫sin^5(x)/cos(x) dx

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Integrate ∫x^3 sin(arc tan(x^4))/(1+x^8) dx

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Florida International U: Find derivatives ...defined implicitly ... (a)-(c)

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