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trig Write each expression as an equivalent algebraic expression involving only x.
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2nd/2ways: count perm Show P(n,2)+P(n,1)=n^2
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trig Show ...
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#6 2019 MIT Integration Bee Final
AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^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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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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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
1st/2ways: r-Permutations
3rd/3ways: sum Show 1+2+3+...+n = n(1+n)/2
Growing patterns #3
2nd/2ways: Evaluate trig integral ∫1/(sin(x) + cos(x)) dx
3rd/3 parts: Growing patterns
2 ways: exp integral ∫(p^x + q^x)/r^x dx
trig integral ∫1/(cos(x)(1+cos(x)) dx
Integrate ∫x^3 sin(arc tan(x^4))/(1+x^8) dx
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2nd/2ways: r-Permutations
2 ways: Derivative √ (1+√ (1+√ x)))
COMMON MISTAKE: trig integral sin^2(x) dx ≠ sin^3(x)/3 + c