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Screen Recording 2024-02-22 at 12.00.24 AM

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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Swinburne U 2nd way: e^(-e^x) e^x dx
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Swinburne U 2nd way: e^(-e^x) e^x dx

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2nd way: integral ∫ log √x(x^n) 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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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 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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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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Review: Linear form, Quadratic form & Bilinear form
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Review: Linear form, Quadratic form & Bilinear form

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...
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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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😘😘😘
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😘😘😘

DJRAFIQIDJRAFIQI

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sqrt integral ∫(√x+1)/(x+√x) dx
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sqrt integral ∫(√x+1)/(x+√x) dx

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trig Evaluate each expression below withOUT using a calculator.
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trig Evaluate each expression below withOUT using a calculator.

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2nd/2 ways: #1 2019 MIT Integration Bee Final
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2nd/2 ways: #1 2019 MIT Integration Bee Final

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

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Alternate way: sq root integral ∫1/√((x-α)(x-β)) dx
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Alternate way: sq root integral ∫1/√((x-α)(x-β)) dx

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UT Austin: sq root integral ∫1/((√x) (1+ √x))dx
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UT Austin: sq root integral ∫1/((√x) (1+ √x))dx

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1st/2ways: Taylor series of sin(x)
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1st/2ways: Taylor series of sin(x)

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2nd way: ∫cos(x)/√(sin^2(x)+4sin(x)+3) dx
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2nd way: ∫cos(x)/√(sin^2(x)+4sin(x)+3) dx

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Differentiate the function y= x^3 (1+x)^2 /((1-x)^4 (1+2x)^2)
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Differentiate the function y= x^3 (1+x)^2 /((1-x)^4 (1+2x)^2)

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Alternate way: exp derivative x^n
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Alternate way: exp derivative x^n

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Alternate way: derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2-xy1=a^2y
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Alternate way: derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2-xy1=a^2y

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