mth.122.handout.04

# Lower case greek letter used in mathematics alpha α

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Lower case greek letter used in mathematics. alpha = α , beta = β , gamma = γ , delta = δ , epsilon = , var epsilon = ε , zeta = ζ , eta = η =, theta = θ , var theta = ϑ , iota = ι , kappa = κ , lambda = λ , mu = μ , nu = ν , xi = ξ , pi = π , var pi = \$ , rho = ρ , var rho = % , sigma = σ , var sigma = ς , tau = τ , upsilon = υ , phi = φ , var phi = ϕ , chi = χ , psi = ψ , omega = ω . Upper case Greek letters used in mathematics: gamma = Γ, delta = Δ, theta = Θ, lambda = Λ, xi = Ξ, pi = Π, sigma = Σ, upsilon = Υ, phi = Φ, psi = Ψ, Omega = Ω. 6

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In[8]:= Integrate @H x^2 + 2 L ê HH x - 1 L H 2 x - 8 L H x + 2 L L , x D Out[8]= 1 ÅÅÅÅ 2 J Log @ - 4 + x D - 1 ÅÅÅÅ 3 Log @ - 1 + x D + 1 ÅÅÅÅ 3 Log @ 2 + x DN In[9]:= Integrate @H x^3 + 1 L ê H x^2 - 4 L , x D Out[9]= x 2 ÅÅÅÅÅÅ 2 + 9 ÅÅÅÅ 4 Log @ - 2 + x D + 7 ÅÅÅÅ 4 Log @ 2 + x D In[10]:= Integrate @H 3 x - 9 L ê HH x - 1 L H x + 2 L ^2 L , x D Out[10]= 3 J - 5 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅ 3 H 2 + x L - 2 ÅÅÅÅ 9 Log @ - 1 + x D + 2 ÅÅÅÅ 9 Log @ 2 + x DN In[11]:= Integrate @H 18 L ê HH x + 3 L H x^2 + 9 L L , x D Out[11]= 18 J 1 ÅÅÅÅÅÅÅ 18 ArcTan A x ÅÅÅÅ 3 E + 1 ÅÅÅÅÅÅÅ 18 Log @ 3 + x D - 1 ÅÅÅÅÅÅÅ 36 Log @ 9 + x 2 DN In[12]:= Apart @H x^2 - 2 L ê HH x + 2 L H x^2 + 4 L ^3 LD Out[12]= 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅ 256 H 2 + x L + 3 H - 2 + x L ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅ 4 H 4 + x 2 L 3 + 2 - x ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅ 32 H 4 + x 2 L 2 + 2 - x ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅ 256 H 4 + x 2 L In[13]:= Apart @H x^2 + 2 L ê HH x - 1 L H 2 x - 8 L H x + 2 L LD Out[13]= 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅ 2 H - 4 + x L - 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅ 6 H - 1 + x L + 1 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅ 6 H 2 + x L In[14]:= Apart @H x^3 + 1 L ê H x^2 - 4 LD Out[14]= 9 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅ 4 H - 2 + x L + x + 7 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅ 4 H 2 + x L In[15]:= Apart @H 3 x - 9 L ê HH x - 1 L H x + 2 L ^2 LD Out[15]= - 2 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅ 3 H - 1 + x L + 5 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ H 2 + x L 2 + 2 ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅ 3 H 2 + x L In[16]:= Apart @H 18 L ê HH x + 3 L H x^2 + 9 L LD Out[16]= 1 ÅÅÅÅÅÅÅÅÅÅÅ 3 + x + 3 - x ÅÅÅÅÅÅÅÅÅÅÅÅÅ 9 + x 2 In[17]:= Apart @H x^2 - 2 L ê HH x + 2 L H x^2 + 4 L ^3 LD Out[17]= 1
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