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

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LibZon

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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2nd way: integral ∫ log √x(x^n) dx

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

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

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Screen Recording 2024-05-18 at 12.32.05 AM

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Show ∫1/(a+btan(x)) dx = ...

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alternate way: ∫ √(x^2+a^2 )dx via "expressing in 2 ways"

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yiyuqingkuang

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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