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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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2nd/2 parts: Mean 1+2+3+...+n is just (1+n)/2. Why?
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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logic Idempotent law show x=xVx
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trig Write each expression as an equivalent algebraic expression involving only x.
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integration bee 2014 UNSW: 4th way: e^x(cos(x)+sin(x)) dx
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#7 2023: MIT Integration Bee Quali Exam: integral ∫x^3 sin(x^2) dx
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3 picture views of the sum ... 1+2+3+...+n
3 ways: exp integral e^(2x)/(1+e^x) dx
2nd/3ways: derivative If f(x)=(x-a)(x-b)(x-c), show f'(x)/f(x)=1/(x-1)+1/(x-b)+1/(x-c)
#17 2020 MIT Integration Bee Quali Exam:
1st/3ways: derivative If f(x)=(x-a)(x-b)(x-c), show f'(x)/f(x)=1/(x-1)+1/(x-b)+1/(x-c)
3 ways: If y=x/(1+x^2) find dy/dx.
3rd/10parts: Exclusive disjunction
If ∫ 2^(1/x)/x^2 dx = a 2^(1/x) +C, then a is?
Show ∫1/(a+btan(x)) dx = ...
[January] Sasaki & Miyano Episode 8 Preview [MCE Chinese Subbing Team]
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trig Prove each identity ... 1) to 10)
2nd way: trig integral ∫sin^6(ax+b) cos^6(ax+b) dx