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5 ways: integral ∫a^(px+q) 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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Penn. State U: Suppose the p.m.f of discrete random variable X is ...
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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exp integral ∫10^x e^(10x) dx
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integral exp ∫e^(mx)/(x^n) dx via Reduction formula
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Lamar U: trig integral ∫cos^5(2t) sin^2(2t) dt
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Roorkee 1976 RET 1991Hindustan: trig integral 1/(sin^2(x) cos^2(x)) dx
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8Screen Recording 2023-12-07 at 1.55.57 AM
2nd way: trig integral ∫1/(1+sec(x)) dx
trig integral sin(x+sin(x))-sin(x-sin(x)) dx
#17 2022 MIT Integration Bee Qualifying Exam
UC Davis: integrate sin(x)/(1+sin(x)) dx
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2nd way: integral tan(x)/(1+tan(x)) dx
derivative x^√x
prob stat: Let J & K be independent events. P(J|K)=0.3. Find P(J)