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Review: trig tan(x+360)= tan(x) & tan(x+180)=tan(x)
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trig Write each expression as an equivalent algebraic expression involving only x.
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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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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
2nd way: integral ∫ log √x(x^n) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
2nd part: n^2 = (tn - tn-1)^2 where tn = nth triangular number
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Review: trig sin(x+180)= -sin(x) & cos(x+180)=-cos(x)
2nd/2 way: Expand e^sin(x) by Maclaurin's Theorem
COMMON MISTAKE!: exp derivative d/dx(a^x) ≠ x a^(x-1)
Solve cos^2(x) dy/dx +y = tan(x) via Integrating factor[IF]
exp derivative e^(ax+b)/2^(ax)
integral ∫x^3/(1-x^8) dx
trig integral Find cos^2(x) sin(x) dx
3 ways: derivative e^y=x
derivative differentiate √((x-3)(x^2+4)/(3x^2+4x+5))
Pantun Melayu [Buah cempedak di luar pagar]
2 ways: exp integral p^(qx+r) dx