2 ways: log derivative log3(x)

3rd/3ways: trig integral ∫sec(x) dx

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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

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

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2nd way: integral ∫ log √x(x^n) dx

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MIT Integration Bee Quali Exam 2023 #7: integral

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RPReplay_Final1791959997

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2nd/2 ways: Alternate way: Given 2 points, find equation of st line passing the ..

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RPReplay_Final1791957727

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2 ways: diff eq Solve dy/dx-x^2=0

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3rd/3 ways: trig integral ∫ sin(ax+b) dx

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UC Davis #14: integral ∫x √(4-x) dx

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

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exp trig derivative x^x sin(x)

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2nd/2ways: count perm Show P(n,n)=P(n,n-1)

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