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Lamar U: trig integral ∫cos^5(2t) sin^2(2t) dt
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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2nd way: integral ∫ log √x(x^n) dx
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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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If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0
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1st/3parts: Mean of 1,2,3,...,n SAME as Mean 1,n
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#6 2019 MIT Integration Bee Final
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2nd/2 parts: Mean 1+2+3+...+n is just (1+n)/2. Why?
1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+sin^2(x)) dx
1st/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)
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log sq root integral ∫ln(√ x^3)/√ √ x dx
trig integral ∫cos(x) sin(x)/(cos^2(x)-1) dx
Screen Recording 2024-02-22 at 10.09.39 PM
trig integral ∫3e^(2x)/(1+e^(4x)) dx
If y=a e^(mx) + b e^(-mx), show that y2=m^2y
exp integral ∫e^x/((a+e^x)(b+e^x)) dx
NYU: 2 ways integral ∫(x^2 + 2x +1) dx
trig integral ∫sin(2x) cos(2x)/(9-cos^4(2x)) dx