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1st/2ways: 1+2+3+...+(n-1)+n+(n-1)+...+3+2+1 = n^2
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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1st way: exp ∫(e^x)/x (1+x log(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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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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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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2nd/2parts example Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n
2nd way: integral ∫ 1/(5x^2 -3x +7) dx with BONUS
#6 2019 MIT Integration Bee Final
2 ways: integral (3+5x)/(x(x-1)) dx
2 ways: ∫ 1/(10x^2 -x-21) dx
2 ways of "counting" (a+b)^2 = a^2+2ab+b^2
exp integral ∫1/(e^(ax+b) (1+e^(ax+b)) dx
trig integral ∫sin(2x) cos(2x) / (9-cos^4(2x)) dx
alternate way: count sum 1+3+5+ ... +(2n-1)
Add Math: Your teacher forgot to tell you ...
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exp integral e^x (f(x) + f'(x)) dx
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