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juantheron
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Evaluation of $$\int^{\frac{\sqrt{5}+1}{2}}_{1}\frac{x^2+1}{x^4-x^2+1}\ln\left(x-\frac{1}{x}+1\right)dx$$
MHB Definite Integration: $$\int^{\frac{\sqrt{5}+1}{2}}_{1}$$
- Thread starter juantheron
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The integral $$\int^{\frac{\sqrt{5}+1}{2}}_{1}\frac{x^2+1}{x^4-x^2+1}\ln\left(x-\frac{1}{x}+1\right)dx$$ presents challenges in evaluation, prompting discussions on suitable methods. Participants suggest exploring substitution techniques and integration by parts, while others mention numerical approximation as a potential approach. Some have attempted partial fraction decomposition to simplify the integrand. The complexity of the logarithmic term adds to the difficulty, leading to considerations of series expansion. Overall, the thread emphasizes the need for innovative strategies to tackle this integral effectively.
Hello!
I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem.
Given:
##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0##
##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1##
##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0##
I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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