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integral exp ∫e^(mx)/(x^n) dx via Reduction formula
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logic Idempotent law show x=xVx
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2
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Review: Product to Sum Identities
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"baby" fact: exp even odd e^x
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I.B.P Derivation [Integration By Parts]
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2nd/2ways: [k map] logic Simplify the Boolean function F=A'B'C+A'BC+AB'
Alternate way: trig integral ∫sec(x) dx= ln(tan(/π4+x/2)) + c
4th/4ways: trig derivative sin(x)
3rd/3ways: exp Derivative x^x
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derivative log f(g(x)) (p(r(x)))
2 ways: exp integral ∫(p^x + q^x)/r^x dx
trig integral ∫sin^2(x)/cos^6(x)) dx
Write 1^2-2^2+3^2-4^2+5^2-6^2+7^2 using summation or product notation
4 ways: exp integral ∫a^(bx+c) dx
2nd/2 ways: trig integral ∫sin^3(x) dx
2nd way: Evaluate integral ∫x^2/√(19-x^2) dx
2 ways: derivative log3(x)