trig integral ∫sin(1/x^2)/x^3 dx

If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0

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trig Write each expression as an equivalent algebraic expression involving only x.

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1st way: exp ∫(e^x)/x (1+x log(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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2nd way: integral ∫ log √x(x^n) dx

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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Review Add Math: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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3 ways: trig Show sec(2x)=sec^2(x)/(2-sec^2(x))

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Integrate ∫x^3 sin(arc tan(x^4))/(1+x^8) dx

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5th/5ways: triangular num: Show t(n-1) + tn = n^2 where tn = nth triangular number

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3rd/3 ways: Express (4x-17)/((x+4)(2x-3)) in partial fractions via withOUT cover rule

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1st/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)

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Difference of 2 nonconsecutive triangular numbers

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2nd/2parts: Review: Equation of a straight line passing through the point (x1,,y1)...

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9Screen Recording 2023-12-02 at 2.43.56 AM

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derivative (f(x))^n vs n^(g(x)) vs (f(x))^g(x)

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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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2 ways: log exp derivative ln(x) e^(2ln(x))

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UT Austin: trig integral ∫cos(√x)/((√x) sin^2(√x)) dx

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