2nd way: trig integral ∫ 1/( √3 sin(x) + cos(x)) dx

prob stat: The following frequency table gives the values obtained

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1st way: exp ∫(e^x)/x (1+x log(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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The sum of 3 numbers in AP is 15 & the sum of their squares is 3. Find the numbers.

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A random variable X has the following parameters: E(X)=a & Var(X)=2a^2-1 a∈R

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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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2nd way: sq rt integral ∫(√x)/(x+1) dx

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Lamar U #12 trig integral sec^4(2t)/tan^9(2t) dt

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Conversion: Permutation - Combination vice versa

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4 ways: trig integral ∫tan(x) dx

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18+ arya voice

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#19 2010 MIT Integration Bee Qualifying Exam

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trig integral ∫x/(1+x) dx vs ∫cos(x)/(1+cos(x)) dx

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#3 2023 MIT Integration Bee Qualifying Exam

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alternate way: count sum 1+2+3+ ... +n

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#23 2019 MIT Integration Bee Final

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2 ways: Derivative √ (1+√ (1+√ x)))

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UC Davis #14: integral ∫x √(4-x) dx

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alternate way: count sum 1+3+5+ ... +(2n-1)

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