2nd Alternate trig ∫integral sin(x) dx

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

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1st/4 ways: integral ∫1/(x + √x) dx

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

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

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Screen Recording 2024-05-11 at 8.58.53 PM

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Screen Recording 2024-02-22 at 10.30.06 PM

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5th/5ways: triangular num: Show t(n-1) + tn = n^2 where tn = nth triangular number

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UT Austin: sq root ∫(1+√x)^3/√x dx

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Alternate way exp derivative (logf(x)(g(x)))^a

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1st/2ways: Taylor series of sin(x)

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trig integral ∫1/(1+cos(ax+b)) dx

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Screen Recording 2024-02-22 at 10.45.08 PM

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2nd/2ways: r-Permutations

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If u=a+ib is a complex #, then complex conjugate of u*=a-ib. ...

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2 ways: Show logb^n(a)=1/n logb(a)

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2nd way: Express (4x-17)/((x+4)(2x-3)) in partial fractions via

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UT Austin: trig sq root integral ∫1/(sin(x) + cos(x)) dxsin(√x)/√(x cos^3(√x)) dx

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