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2 ways: trig exp derivative e^(sin(x)) sin(e^x)
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1st/3parts: Checkpoint 1.1 STPM Math T Sem2
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integral ∫ x dx withOUT using Power rule.
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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Pantun Melayu [Buah cempedak di luar pagar]
MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
trig Write each expression as an equivalent algebraic expression involving only x.
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1st/2ways: logic Import-Export
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2nd/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via "picture".
alternate way: count sum 1+3+5+ ... +(2n-1)
Derivative (af(x)+b)^(pg(x)+q)
2nd/2ways: r-Permutations
3rd/3ways: sum Show 1+2+3+...+n = n(1+n)/2
1st/3ways: trig integral ∫sec(x) dx
Example: Find the sum
1st/2ways: Find trig integral ∫sec^2(x)/csc^2(x) dx
OSU Math 1151 Practice4: Compute the derivative
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Review count Common mistake Rearrangement LOOT=4!/2 vs LULL NOT = 4!/3