mathematica

How to set the function F(x) = 2x^2-2x-2 при x<=2 F(x) = sqrt(x-1) при x=2

How to choose a replacement that leads the integral of a given function to the integral of a rational function and decompose it into simple fractions by the method of indefinite coefficients using wolfram mathematica?

I want to take a derivative, but it throws this error, writes can't use this variable, I don't understand why: What could be the reason?

I have five DXF files with various geometric figures. Are squares with a different geometric shape in each DXF file ... F ... ometries and do some assembly like this? The animation is illustrative only. It was created just for ease of understanding.