Hurricane Electric Mathematics

[8𝑒(𝑥)√(xˣ⁺¹(𝑥−1)!)-(𝑥−8𝑥²−4𝑥ln𝑥−ln²𝑥−(4𝑥+2ln𝑥)ln2𝜋)]

asked by guest
on Nov 15, 2024 at 6:05 pm

You asked:

Evaluate the expression:

8 \cdot e\left( x \right) \cdot \sqrt{{x}^{x + 1} \cdot \left( x - 1 \right)!} - \left(x - 8 {x}^{2} - 4 x \ln\left( x \right) - {\ln\left( x \right)}^{2} - \left(4 x + 2 \ln\left( x \right)\right) \cdot \ln\left( 2 \pi \right)\right)

MathBot Answer:

Evaluated

$\displaystyle 8 \cdot e\left( x \right) \cdot \sqrt{{x}^{x + 1} \cdot \left( x - 1 \right)!} - \left(x - 8 {x}^{2} - 4 x \ln\left( x \right) - {\ln\left( x \right)}^{2} - \left(4 x + 2 \ln\left( x \right)\right) \cdot \ln\left( 2 \pi \right)\right) = 8 x^{2} + 4 x \log{\left(x \right)} - x + 8 \sqrt{x^{x + 1} \left(x - 1\right)!} e{\left(x \right)} + \left(4 x + 2 \log{\left(x \right)}\right) \log{\left(2 \pi \right)} + \log{\left(x \right)}^{2}$

Expanded

$8 \cdot e\left( x \right) \cdot \sqrt{{x}^{x + 1} \cdot \left( x - 1 \right)!} - \left(x - 8 {x}^{2} - 4 x \ln\left( x \right) - {\ln\left( x \right)}^{2} - \left(4 x + 2 \ln\left( x \right)\right) \cdot \ln\left( 2 \pi \right)\right) = 8 x^{2} + 4 x \log{\left(x \right)} - x + 4 x \log{\left(2 \right)} + 4 x \log{\left(\pi \right)} + 8 \sqrt{x^{x} x \left(x - 1\right)!} e{\left(x \right)} + \log{\left(x \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(x \right)} + 2 \log{\left(x \right)} \log{\left(\pi \right)}$

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