2 way: exp integral e^(ax+b)/1+e^(ax+b)) dx

sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))

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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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Diff Equ: Solve y-xdy/dx=b(1+x^2dy/dx)) via integrating factor [IF]

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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n

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Really don’t want to go to work and have no marketable skills? Then you can try these few methods! #

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logic How can we check our Boolean simplification is done correctly?

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2010 #2 MIT Integration Bee

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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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trig integral ∫1/(sin(ax) cos(ax)) dx

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1st/2 way: Expand e^sin(x) by Maclaurin's Theorem

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UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

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Screen Recording 2024-02-22 at 10.23.21 PM

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Screen Recording 2024-02-22 at 10.18.05 PM

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derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2 - xy1 = a^2y.

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Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx

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Discrete rv X has the following prob. distribution

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Screen Recording 2024-02-22 at 10.13.28 PM

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2 ways: Find logarithm of 5 to the base 5 √5.

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derivative If y=acos(log(x)) + bsin(log(x)), prove that x^2y2+xy1+y=0

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