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Solving $x^2 + 18x + 30 = 2 \sqrt{x^2 + 18x + 45}$? (1983 AIME problem 3)

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#polynomials #contest-math #quadratics #substitution #quartics
138
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Integration by substitution of an improper integral, where did I go wrong?

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#integration #substitution
300
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Evaluate $\int_{1}^{2} \ \frac{\arctan (x)}{\arctan \left (\frac{1}{x^2-3x+3} \right )} dx$

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#calculus #integration #definite-integrals #substitution
158
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Irrational equation system

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#algebra-precalculus #systems-of-equations #radicals #substitution
457
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The converse of the axiom of extensionality

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#set-theory #first-order-logic #substitution
85
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How to prove that $\frac{a^2 + b^2 -2}{a + b - 2} < 1 + b$ if $a < b$ and $a, b > 1$?

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#algebra-precalculus #elementary-number-theory #inequality #fractions #substitution
57
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Integral involving multiple variables

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#calculus #integration #indefinite-integrals #substitution
762
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Problems with limits and asymptotic notation

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#limits #asymptotics #substitution
136
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Inequality with powers of 2

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#inequality #exponential-function #integers #substitution #muirhead-inequality
77
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Integral of function from $0$ to $\pi$ using $\sin x=t$ substitution

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#integration #definite-integrals #substitution #trigonometric-integrals
330
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Cubic Equation With Complex Roots

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#functions #trigonometry #complex-numbers #substitution #cubics
648
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Irreducibility of $x^3-6x-2$ in $Q[x]$

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#abstract-algebra #polynomials #roots #substitution #discriminant
171
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Solving $\int(x^2 + 1)^7x^3{\mathrm d}x$ without expansion

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#calculus #integration #polynomials #indefinite-integrals #substitution
54
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how do I manipulate natural logs in my integration

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#integration #logarithms #absolute-value #substitution
263
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Trig substitution domain

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#substitution #trigonometric-integrals

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