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3 ways: derivative log(x+ (1+√(x^2)))
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2nd/2ways: [k map] logic Simplify the Boolean function F=A'B'C+A'BC+AB'
2 ways: log derivative log3(x)
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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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(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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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)
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2nd/2ways: Taylor series of sin(x) [Maclaurin's series]
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2nd/2ways: r-Permutations
1st/2ways: r-Permutations
2nd/2ways: Evaluate trig integral ∫1/(sin(x) + cos(x)) dx
1st/3ways: derivative If f(x)=(x-a)(x-b)(x-c), show f'(x)/f(x)=1/(x-1)+1/(x-b)+1/(x-c)
Screen Recording 2024-02-16 at 9.17.40 PM
Which pairs are equivalent via truth table?
UT Austin: ∫x (1-x^2)^1/4 dx
2 ways: Find ∫(ax^x+bx+c) dx
Alternate way: trig integral ∫sec(x) dx= ln(tan(/π4+x/2)) + c