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4 ways: exp integral ∫a^(bx+c) dx
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]
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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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2nd/3ways: trig integral ∫sec(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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Common log mistake: logb(xy^n) ≠ nlogb(xy)
log sq root integral ∫ln(√ x^3)/√ √ x dx
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alternate way: count sum 1+2+3+ ... +n
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4th/4parts: Maclaurin Series [ahp kia]
1st/2ways: add math sum a + (a+d) + (a+2d) + ... + (a+(n-1)d) ?
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2nd/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)
2nd part/3parts: Mean of -11,-2,7,...,70 SAME as Mean -11 & 70
sq root log derivative √ ln(f(x))
If 2^x + 2^y = 2^(x+y), then dy/dx ?
1st/2parts 3 ways: tn-1 + tn = n^2 where tn = nth triangular number
Mohammad Ali Jinnah University: Integrate the followings.
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integral ∫x dx withOUT using power rule
2 ways: trig integral ∫ sec^2(x) csc^2(x) dx