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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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2nd way: integral ∫ log √x(x^n) dx
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logic: De Morgan's Law
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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...
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Swinburne U 2nd way: e^(-e^x) e^x dx
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1st/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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Review: Linear form, Quadratic form & Bilinear form
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trig Write each expression as an equivalent algebraic expression involving only x.
exp integral e^x (f(x) + f'(x)) dx
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2nd/2ways: count perm Show P(n,n)=P(n,n-1)
Example: Find the sum
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integral Find ∫1/(9-4x^2) dx
1st/2ways: logic Import-Export
Growing patterns #3
trig integrals ∫cot(ax+b) dx vs ∫cot^2(ax+b) dx
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2 ways: derivative a^f(g(x))
integral ∫e^x(1/x - 1/x^2) dx
exp trig derivative x^x sin(x)
2nd way: trig integral ∫1/(sin(x) cos^2(x)) dx