UC Davis #14: trig integral ∫(sin(x)-cos(x))(sin(x)+cos(x))^5 dx

STPM Math T Sem.2 Exponential fun: Find the derivative (19)-(40)

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🪔 Happy Deepavali 🪔 [Nov-12-2023]

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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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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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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6th form Pure Math: Evaluate the integrals

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4 ways: exp integral ∫a^(bx+c) dx

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1st/2 ways: derivative y=(ln(x))^x

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UT Austin: trig integral ∫cot(x) csc^2(x) dx

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Alternate way: trig integral ∫cos(x) dx

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3rd/3ways: trig integral ∫sec(x) dx

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The University of Maine: rational function integral compute

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Oggy ep34

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2nd/2ways: count perm Show P(n,2)+P(n,1)=n^2

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prob & stat: Show ...

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Suppose f & g are positive functions. Obtain the product rule for (fg)' by differentiating ...

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