3rd/3ways: count comb A set with n elements has 2^n subsets

diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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trig Write each expression as an equivalent algebraic expression involving only x.

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3 ways: derivative e^y=x

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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Alternate way: log integral ∫1/(bx+xln(ax^r)) dx

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But I suddenly realized that I am not anyone's best friend.

yuleshen

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Pure love fan circle culture has set its sights on Mortal Journey to Immortality. Anti-pure love fan

machirise_04

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CMU: Find these integrals (a)-(b)

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Screen Recording 2024-02-16 at 8.23.14 PM

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Diff Eq: Solve sec(x) dy/dx=y+sin(x) via Integrating factor [IF]

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2nd way: integral ∫1/(a + √√b (x^2)) dx

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trig Show sec^4(x)-tan^4(x) = sec^2(x)+tan^2(x)

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trig integral ∫sec^2(x)/tan(x) dx vs ∫tan(x)/sec^2(x) dx

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3 ways: rational function integral ∫2x/(x+1)^2 dx

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【MMD】APPLE PIE【KS-style Hatsune Miku】

Rshixun

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2nd/2 parts: sum Find the sum 2,3,14,24,37,... nth term

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If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0

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