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2nd way: sq rt log integral ∫√√√(x) ln(x) dx
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2nd way: integral ∫ log √x(x^n) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(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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trig integral ∫sec(x) dx =
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UT Austin: trig integral ∫(1/x^2) sin(1/x) cos(1/x) dx
2024 MIT Integration Bee Final
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1st way: count values nPn, nP(n-1), nP(n-2)
2nd/3ways: sum Show 1+2+3+...+n=n(1+n)/2
3rd way: rational function integral ∫x^3/√ (1+x^2) dx
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integral ∫e^x(1/x - 1/x^2) dx
Alternate way: trig integral ∫cot(x) csc^6(x) dx ... just in 1 line.
prob stat: Consider the experiment of tossing a fair coin twice & reading the up face on each toss.
"baby" fact: exp e^(ix)
UC Davis #1: 2 ways Find the length of the graph for y=3x+2 on the closed interval ...
Is 4cos^3(x)-3cos(x) EVEN, ODD, NEITHER, BOTH EVEN & ODD?
prob & stat: Show ...
exp Calculate ∫x^3 3^x dx via IBP
Pascal's triangle nth triangular number [examples]
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