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Lamar U: Derivatives of Exponential & Log Functions Assignment Problems.
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(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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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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2nd way: integral ∫ log √x(x^n) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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1st/2parts 3 ways: tn-1 + tn = n^2 where tn = nth triangular number
Show that ar sinh(x) = ln(x + √ (x^2+1))
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Lamar U: Derivatives of Exponential & Log Functions Practice Problems.
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integral ∫√(x-a)/x dx
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logic: If p then q ...
3rd/3ways: sum Show 1+2+3+...+n = n(1+n)/2
3 ways: If y=x/(1+x^2) find dy/dx.
2nd way: Evaluate ∫a/(b+ce^x)dx
2nd/2ways: Evaluate trig integral ∫1/(sin(x) + cos(x)) dx
integrate ∫e^x (1+sin(x))/(1+cos(x)) dx
1st/2ways: Find trig integral ∫sec^2(x)/csc^2(x) dx
rational function integral x/(x-√(x^2-1)) dx
1st/2 ways: derivative y=(ln(x))^x