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10 cards from this deck
Decompose complex rational expressions into simpler fractions
Linear or irreducible quadratic terms
Decompose, determine constants, integrate each term
Axโa+Bxโb\frac{A}{x-a} + \frac{B}{x-b}xโaAโ+xโbBโ
Axโa+B(xโa)2\frac{A}{x-a} + \frac{B}{(x-a)^2}xโaAโ+(xโa)2Bโ
Ax+Bx2+1\frac{Ax+B}{x^2+1}x2+1Ax+Bโ
lnโกโฃxโฃ+C\ln|x| + Clnโฃxโฃ+C
1aarctanโก(xa)+C\frac{1}{a} \arctan(\frac{x}{a}) + Ca1โarctan(axโ)+C
12lnโก(x2+a2)+C\frac{1}{2} \ln(x^2+a^2) + C21โln(x2+a2)+C
Missing the constant of integration +C+C+C
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