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Logical equivalent involving ... tautology & contradiction
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Integrate ∫x^3 sin(arc tan(x^4))/(1+x^8) dx
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Alternate way: Evaluate exp integral ∫1/√(1-e^(2x)) dx
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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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(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 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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trig integral a) Show that sin(t) cos(t)=1/2 sin^2(t)+c
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2nd/2ways: count perm Show P(n,2)+P(n,1)=n^2
trig Prove each identity ... 1) to 10)
Quickie: In music, there is circle of 5ths ... In calculus, there is circle ...
Princeton U: Compute the integral ∫sin^5(x)/cos(x) dx
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Vandermonde's Identity
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Wanna know function that is BOTH even AND odd? Here you go ...
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3rd/4ways: trig derivative sin(x)
log derivative ln(x) via chain rule
2nd way: trig differentiate (log(x))^cos(x)