Elements of Chemical Reaction Engineering, 6th Edition

A. Numerical Techniques

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A.1 Useful Integrals in Chemical Reactor Design

$\begin{matrix} \int_{0}^{χ} \frac{d x}{1 - x} = \ln \frac{1}{1 - x} & (A-1) \end{matrix}$

$\begin{matrix} \int_{x_{1}}^{x_{2}} \frac{d x}{(1 - x)^{2}} = \frac{1}{1 - x_{2}} - \frac{1}{1 - x_{1}} & (A-2) \end{matrix}$

$\begin{matrix} \int_{0}^{x} \frac{d x}{(1 - x)^{2}} = \frac{χ}{1 - x} & (A-3) \end{matrix}$

$\begin{matrix} \int_{0}^{x} \frac{d x}{1 + ɛ x} = \frac{1}{ɛ} \ln (1 + ɛ x) & (A-4) \end{matrix}$

$\begin{matrix} \int_{0}^{x} \frac{(1 + ɛ x) d x}{1 - x} = (1 + ɛ) \ln \frac{1}{1 - x} - ɛ x & (A-5) \end{matrix}$

$\begin{matrix} \int_{0}^{x} \frac{(1 + ɛ x) d x}{(1 - x)^{2}} = \frac{(1 + ɛ) x}{1 - x} - ɛ \ln \frac{1}{1 - x} & (A-6) \end{matrix}$

$\begin{matrix} \int_{0}^{x} \frac{(1 + ɛ x)^{2} d x}{(1 - x)^{2}} = 2 ɛ (1 + ɛ) \ln (1 - x) + ɛ^{2} x + \frac{(1 + ɛ)^{2} x}{1 - x} & (A-7) \end{matrix}$

$\begin{matrix} \begin{matrix} \int_{0}^{x} \frac{d x}{(1 - x) (Θ_{B} - x)} = \frac{1}{Θ_{B} - 1} In \frac{Θ_{B} - x}{Θ_{B} (1 - x)} & Θ_{B} \neq 1 \end{matrix} & (A-8) \end{matrix}$

$\begin{matrix} \int_{0}^{W} (1 - α W)^{1 / 2} d W = \frac{2}{3 α} [1 - (1 - α W)^{3 / 2}] & (A-9) \end{matrix}$

$\begin{matrix} \int_{0}^{x} \frac{d x}{a x^{2} + b x + c} = \frac{- 2}{2 a x + b} + \frac{2}{b} & for b^{2} = 4 a c (A-10) \end{matrix}$

$\begin{matrix} \int_{0}^{x} \frac{d x}{a x^{2} + b x + c} = \frac{1}{a (p - q)} \ln (\frac{q}{p} \cdot \frac{x - p}{x - q}) & for b^{2} > 4 a c (A-11) \end{matrix}$

where p and q are the roots of the equation.

$\begin{matrix} \begin{matrix} \begin{matrix} {a x}^{2} + b x + c = 0, & that is, p, q \end{matrix} = \frac{- b \bar{+} \sqrt{b^{2} - 4 a c}}{2 a} \\ \int_{0}^{x} \frac{a + b x}{c + g x} d x = \frac{b x}{g} + \frac{a g - b c}{g^{2}} In \frac{c + g x}{c} \end{matrix} & (A-12) \end{matrix}$

A.2 Equal-Area Graphical Differentiation ...

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Elements of Chemical Reaction Engineering, 6th Edition by H. Scott Fogler

A. Numerical Techniques

A.1 Useful Integrals in Chemical Reactor Design

A.2 Equal-Area Graphical Differentiation ...

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