Screen Recording 2024-02-16 at 8.34.08 PM

1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+sin^2(x)) dx

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2 ways: The following measurements were taken by an antique dealer as he weighted to the ...

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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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lim x/e^x? as x→∞

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

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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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3 ways: Find 1+2+3+ ... + n^2.

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2nd way: integral ∫(6+4x--2x^2) dx via 1) complete sq 2) then trig. sub

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#12 UC Davis: Find the length of the graph for x=ln(y)=y^2/8 on the closed interval ...

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1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]

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Rutgers U: Verify using calculus

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2nd way: integral 1) ∫1/√(a - √b x^2)dx vs 2) ∫1/√(a - √b x^2) dx

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Rutgers U: 2nd way compute ∫√(x^2 -2)/x dx

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NYU: 3 ways ∫(1+ln(x))/x dx

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

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matrix example: How to select the column you want ...

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A bag contains 5 red balls & 3 green balls. A ball is selected at random &

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2nd way: exp integral e^3x/(e^x +2) dx withOUT u-sub

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Lamar U 2nd way: evaluate trig integral ∫csc(x/2) cot(x/2)(csc^6(x/2)+3csc^4(x/2)-8csc(x/2)) dx

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