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@ Maywaters
2024-07-11 00:21:12$$\begin{array}{l}{{y_{1}\left({\boldsymbol{x}}\right)=1+\int_{0}^{x}{\frac{t}{{\boldsymbol{x}}^{2}+{\boldsymbol{t}}^{2}}}d t=1+{\frac{1}{2}}!!\int_{0}^{x}{\frac{2t}{{\boldsymbol{x}}^{2}+{\boldsymbol{t}}^{2}}}d t=1+{\frac{1}{2}}!!\int_{0}^{x}{\frac{1}{{\boldsymbol{x}}^{2}+{\boldsymbol{t}}^{2}}}d\left(t^{2}\right)=}}\ {{=1+{\frac{1}{2}}{\Bigl(}\ln\left({\boldsymbol{x}}^{2}+{\boldsymbol{x}}^{2}\right)-\ln\left({\boldsymbol{x}}^{2}\right){\Bigr)}=1+{\frac{1}{2}}\ln\left({\frac{2{\boldsymbol{x}}^{2}}{{\boldsymbol{x}}^{2}}}\right)=1+{\frac{1}{2}}\ln\left(2\right)}}\end{array}$$![[Pasted image 20240706143932.webp]]
Carl - 11/06/2023, 23:49 🌟 9 tabletop-games (edited)
