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juantheron
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$\displaystyle \int \frac{e^x}{1+x}dx$
MHB What Is the Indefinite Integral of \( \frac{e^x}{1+x} \)?
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The indefinite integral of \( \frac{e^x}{1+x} \) is non-elementary and is closely related to the exponential integral function. It can be expressed as \( \int \frac{e^x}{1+x}dx = \frac{{\rm{Ei}}(x+1)}{e} + C \). This result highlights the complexity of integrating functions that involve both exponential and rational components. The exponential integral, denoted as Ei, plays a crucial role in this context. Understanding this integral is important for advanced calculus and mathematical analysis.
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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