2nd way: ∫2x/(x+5)^6 dx vs ∫2x (x+5)^6 dx

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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

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sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))

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Review: Arithmetic Series a+(a+d)+(a+2d)+...+(a+(n-1)d)=

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UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

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derivative (f(x)/g(x))^h(x)

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MPPET 1993 BIT Ranchi 1982 Hindusta: trig integral ∫ (1+cos^2(x)/sin^2(x) dx

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

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5 ways: trig Derivative of sin^2(x)

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Lamar U 2nd way: evaluate exp integral ∫e^(8x)(4+e^(4x))^(-3) dx

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3 ways: Derivative x^(-1/x)

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

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trig Show sec^4(x)-tan^4(x) = sec^2(x)+tan^2(x)

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Screen Recording 2024-05-10 at 6.19.39 PM

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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]

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Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction

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