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2nd way: trig integral ∫1/(sin(x) cos^2(x)) dx

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trig integral ∫sin^5(x) dx

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1st/10 parts: Logical disjunction

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(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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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(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 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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How many chords can be drawn through 21 points on a circle?

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

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Growing patterns #2

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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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2 ways: exp integral ∫(p^x + q^x)/r^x dx

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2nd/2ways: Taylor series of sin(x) [Maclaurin's series]

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2nd way: trig integral ∫√(sec^5(x)/sin^3(x)) dx

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#Screen Recording 2024-05-13 at 10.52.38 PM

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A function f is called even if f(-x)=f(x) for ALL x in the domain of f &

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exp integral ∫a^x/b^x dx

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UC Davis: #10 trig integral ∫sin(x)/(1+sin(x)) dx

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