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juantheron
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$\displaystyle \int \frac{x^2\cos^{-1}\left(x\sqrt{x}\right)}{(1-x^3)^2}dx$
MHB Inverse Integral: $\int \frac{x^2\cos^{-1}\left(x\sqrt{x}\right)}{(1-x^3)^2}dx$
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The integral $\int \frac{x^2\cos^{-1}\left(x\sqrt{x}\right)}{(1-x^3)^2}dx$ can be approached using integration by parts, where dv is set to $\frac{x^2}{(1-x^3)^2}$ and u is $\cos^{-1}(x\sqrt{x})$. This method allows for the simplification of the integral by breaking it into more manageable components. The integration by parts technique is highlighted as a suitable strategy for tackling this complex expression. Ultimately, this approach aims to facilitate the evaluation of the 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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