count quick review: Permutation vs Combination

1st/2ways: permutation Show P(n,2)+P(n,1)=n^2

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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Penn. State U: Suppose the p.m.f of discrete random variable X is ...

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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

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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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3 ways: derivative e^y=x

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trig integral ∫sin(2x) cos(2x) / (9-cos^4(2x)) dx

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3 ways: trig Show sec(2x)=sec^2(x)/(2-sec^2(x))

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2 ways: exp integral p^(qx+r) dx

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JEE Main integral x^2/(a+bx)^2 dx

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

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2nd way: ∫2x/(x+5)^6 dx vs ∫2x (x+5)^6 dx

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2nd way: trig integral ∫1/(a+b sin(x)+c cos(x)) dx

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2nd way: trig 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫sin(x)cos(x)cos(4x)cos(8x)cos(16x)cos(32x)cos(64x) dx

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D.C0n4n_1038

lyne minhoney

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trig integral ∫x^2 cos(x^3) e^sin(x^3) dx

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logic: contradiction p∧¬p

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