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2nd way: trig inverse ∫(2012)^x (2012)^ arc (sin(2012)^x)√(1-(2012)^2x) dx
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2nd way: integral ∫ log √x(x^n) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
1st way: exp ∫(e^x)/x (1+x log(x)) dx
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UC Davis: 2nd way differentiate y=(sin(x))^(x^3)
logic implication distribute across disjunction: Show x→(y∨z) ≡ (x→y) ∨ (x→z)
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2nd way: ∫2x/(x+5)^6 dx vs ∫2x (x+5)^6 dx
The number of solutions of the equation x^(log10(x)) = 100x
Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx
2nd way: trig integral (3-tan^2(x))/(cot(x)-3tan(x)) dx
2nd way: trig integral (sin(x)-cos(x))^2 dx
2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1
2nd way: exp integral ∫e^(a√x)/√x dx
2nd way: exp integral ∫e^(1/x)/x^2 dx
2nd way: trig integral ∫1/(a+b sin(x)+c cos(x)) dx
Alternate way: derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2-xy1=a^2y
2 ways: trig exp derivative e^(sin(x)) sin(e^x)
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2nd way: integral ∫x^2 √(x^3+1) dx vs ∫x^3 √(x^3+1) dx
2nd way: trig integral ∫1/(cos^2(x) - sin^2(x)) dx