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TeX (original user input): 

\begin{align}

& {{P}_{i}}=\rho \left( {{x}^{i}} \right){{\Delta }^{d}}x \\

& I(P)=\sum\limits_{i}^{{}}{{}}{{\Delta }^{d}}x\rho \left( {{x}^{i}} \right)\ln \left( {{\Delta }^{d}}x\rho \left( {{x}^{i}} \right) \right)=\sum\limits_{i}^{{}}{{}}{{\Delta }^{d}}x\rho \left( {{x}^{i}} \right)\ln \left( \rho \left( {{x}^{i}} \right) \right)+\sum\limits_{i}^{{}}{{}}{{\Delta }^{d}}x\rho \left( {{x}^{i}} \right)\ln \left( {{\Delta }^{d}}x \right) \\

& \sum\limits_{i}^{{}}{{}}{{\Delta }^{d}}x\rho \left( {{x}^{i}} \right)=1 \\

& \sum\limits_{i}^{{}}{{}}{{\Delta }^{d}}x\rho \left( {{x}^{i}} \right)\ln \left( {{\Delta }^{d}}x \right)=const. \\

\end{align}

TeX (checked): 

{\begin{aligned}&{{P}_{i}}=\rho \left({{x}^{i}}\right){{\Delta }^{d}}x\\&I(P)=\sum \limits _{i}^{}{}{{\Delta }^{d}}x\rho \left({{x}^{i}}\right)\ln \left({{\Delta }^{d}}x\rho \left({{x}^{i}}\right)\right)=\sum \limits _{i}^{}{}{{\Delta }^{d}}x\rho \left({{x}^{i}}\right)\ln \left(\rho \left({{x}^{i}}\right)\right)+\sum \limits _{i}^{}{}{{\Delta }^{d}}x\rho \left({{x}^{i}}\right)\ln \left({{\Delta }^{d}}x\right)\\&\sum \limits _{i}^{}{}{{\Delta }^{d}}x\rho \left({{x}^{i}}\right)=1\\&\sum \limits _{i}^{}{}{{\Delta }^{d}}x\rho \left({{x}^{i}}\right)\ln \left({{\Delta }^{d}}x\right)=const.\\\end{aligned}}

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MathML (43.033 KB / 4.386 KB) :

P i = ρ ⁢ ( x i ) ⁢ Δ d ⁢ x I ⁢ ( P ) = ∑ i Δ d ⁢ x ⁢ ρ ⁢ ( x i ) ⁢ ln ⁡ ( Δ d ⁢ x ⁢ ρ ⁢ ( x i ) ) = ∑ i Δ d ⁢ x ⁢ ρ ⁢ ( x i ) ⁢ ln ⁡ ( ρ ⁢ ( x i ) ) + ∑ i Δ d ⁢ x ⁢ ρ ⁢ ( x i ) ⁢ ln ⁡ ( Δ d ⁢ x ) ∑ i Δ d ⁢ x ⁢ ρ ⁢ ( x i ) = 1 ∑ i Δ d ⁢ x ⁢ ρ ⁢ ( x i ) ⁢ ln ⁡ ( Δ d ⁢ x ) = c ⁢ o ⁢ n ⁢ s ⁢ t . absent subscript 𝑃 𝑖 𝜌 superscript 𝑥 𝑖 superscript Δ 𝑑 𝑥 absent 𝐼 𝑃 subscript 𝑖 superscript Δ 𝑑 𝑥 𝜌 superscript 𝑥 𝑖 superscript Δ 𝑑 𝑥 𝜌 superscript 𝑥 𝑖 subscript 𝑖 superscript Δ 𝑑 𝑥 𝜌 superscript 𝑥 𝑖 𝜌 superscript 𝑥 𝑖 subscript 𝑖 superscript Δ 𝑑 𝑥 𝜌 superscript 𝑥 𝑖 superscript Δ 𝑑 𝑥 absent subscript 𝑖 superscript Δ 𝑑 𝑥 𝜌 superscript 𝑥 𝑖 1 absent subscript 𝑖 superscript Δ 𝑑 𝑥 𝜌 superscript 𝑥 𝑖 superscript Δ 𝑑 𝑥 𝑐 𝑜 𝑛 𝑠 𝑡 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle{{P}_{i}}=\rho% \left({{x}^{i}}\right){{\Delta}^{d}}x\\ \par&\displaystyle I(P)=\sum\limits_{i}{{}}{{\Delta}^{d}}x\rho\left({{x}^{i}}% \right)\ln\left({{\Delta}^{d}}x\rho\left({{x}^{i}}\right)\right)=\sum\limits_{% i}{{}}{{\Delta}^{d}}x\rho\left({{x}^{i}}\right)\ln\left(\rho\left({{x}^{i}}% \right)\right)+\sum\limits_{i}{{}}{{\Delta}^{d}}x\rho\left({{x}^{i}}\right)\ln% \left({{\Delta}^{d}}x\right)\\ \par&\displaystyle\sum\limits_{i}{{}}{{\Delta}^{d}}x\rho\left({{x}^{i}}\right)% =1\\ \par&\displaystyle\sum\limits_{i}{{}}{{\Delta}^{d}}x\rho\left({{x}^{i}}\right)% \ln\left({{\Delta}^{d}}x\right)=const.\\ \par\end{aligned}}}

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MathML (4.59 KB / 497 B) :

Pi=ρ(xi)ΔdxI(P)=∑iΔdxρ(xi)ln⁡(Δdxρ(xi))=∑iΔdxρ(xi)ln⁡(ρ(xi))+∑iΔdxρ(xi)ln⁡(Δdx)∑iΔdxρ(xi)=1∑iΔdxρ(xi)ln⁡(Δdx)=const.

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