[8๐(๐ฅ)โ(xหฃโบยน(๐ฅโ1)!)-(๐ฅโ8๐ฅยฒโ4๐ฅln๐ฅโlnยฒ๐ฅโ(4๐ฅ+2ln๐ฅ)ln2๐)]
You asked:
MathBot Answer:
Evaluated
\(\displaystyle 8 \cdot e\left( x \right) \cdot \sqrt{{x}^{x + 1} \cdot \left( x - 1 \right)!} - \left(x - 8 \cdot {x}^{2} - 4 x \cdot \ln\left( x \right) - {\ln\left( x \right)}^{2} - \left(4 x + 2 \cdot \ln\left( x \right)\right) \cdot \ln\left( 2 \cdot \pi \right)\right) = 8 x^{2} + 4 x \log{\left(x \right)} - x + 8 \sqrt{x^{x + 1} \left(x - 1\right)!} e{\left(x \right)} + \left(4 x + 2 \log{\left(x \right)}\right) \log{\left(2 \pi \right)} + \log{\left(x \right)}^{2} \)
Expanded
\[8 \cdot e\left( x \right) \cdot \sqrt{{x}^{x + 1} \cdot \left( x - 1 \right)!} - \left(x - 8 \cdot {x}^{2} - 4 x \cdot \ln\left( x \right) - {\ln\left( x \right)}^{2} - \left(4 x + 2 \cdot \ln\left( x \right)\right) \cdot \ln\left( 2 \cdot \pi \right)\right) = 8 x^{2} + 4 x \log{\left(x \right)} - x + 4 x \log{\left(2 \right)} + 4 x \log{\left(\pi \right)} + 8 \sqrt{x^{x} x \left(x - 1\right)!} e{\left(x \right)} + \log{\left(x \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(x \right)} + 2 \log{\left(x \right)} \log{\left(\pi \right)}\]
Factored
\[8 \cdot e\left( x \right) \cdot \sqrt{{x}^{x + 1} \cdot \left( x - 1 \right)!} - \left(x - 8 \cdot {x}^{2} - 4 x \cdot \ln\left( x \right) - {\ln\left( x \right)}^{2} - \left(4 x + 2 \cdot \ln\left( x \right)\right) \cdot \ln\left( 2 \cdot \pi \right)\right) = 8 x^{2} + 4 x \log{\left(x \right)} - x + 4 x \log{\left(2 \right)} + 4 x \log{\left(\pi \right)} + 8 \sqrt{x^{x} x \left(x - 1\right)!} e{\left(x \right)} + \log{\left(x \right)}^{2} + 2 \log{\left(2 \right)} \log{\left(x \right)} + 2 \log{\left(x \right)} \log{\left(\pi \right)}\]