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the maid's master anime in english (1-..12)
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integral ∫ x dx withOUT using Power rule.
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2nd/3ways: trig integral ∫sec(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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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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2nd way: integral ∫ log √x(x^n) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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Screen Recording 2024-05-10 at 5.37.05 PM
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alternate way: count sum 1+2+3+ ... +n
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inverse trig integral ∫x^2 arc tan(x^3)/(1+x^6) dx
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2 ways: trig integral ∫ sec^2(x) csc^2(x) dx
2 ways: trig integral ∫ sin^2(ax+b) dx
Vandermonde's Identity
2 ways: trig integral ∫cos^2(x) dx
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prob stat: x̄=∑xk where k=1,2,3,...,n?