3 ways: trig integral ∫sec^2(x) tan(x) dx

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COMMON MISTAKE: (1) logb(m) logb(n) ≠ logb(m+n)

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COMMON MISTAKE: (1) logb(m) logb(n) ≠ logb(m+n)

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(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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3rd/3ways: exp Derivative x^x

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2nd way: derivative x w.r.t x^x. [YES, d(x)/d(x^x)!]

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UC Davis: differentiate y=ln(cos^5(3x^4))

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UC Davis: differentiate y=ln(cos^5(3x^4))

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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exp integral ∫a^x/b^x dx

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exp integral ∫a^x/b^x dx

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Find the number of different 8 letter arrangements that can be made from the letters of the word ..

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Find the number of different 8 letter arrangements that can be made from the letters of the word ..

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1st way: trig derivative (sin(x))^x

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1st way: trig derivative (sin(x))^x

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Genshin Impact Thinking

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2nd/2 ways: [k-map] logic:Simplify the Boolean function F=A+A'B

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2nd/2 ways: [k-map] logic:Simplify the Boolean function F=A+A'B

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2nd way: trig integral ∫1/(sin(x) cos^2(x)) dx

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2nd way: trig integral ∫1/(sin(x) cos^2(x)) dx

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If 4xe^(xy)=y+5sin^2(x) then find the value of y'(0)

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If 4xe^(xy)=y+5sin^2(x) then find the value of y'(0)

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trig integral ∫sin(2x) cos(2x)/(9-cos^4(2x)) dx

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trig integral ∫sin(2x) cos(2x)/(9-cos^4(2x)) dx

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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