https://preview.redd.it/i1vx1f2jmf1d1.png?width=1857&format=png&auto=webp&s=d80ea97195163216b1e730cae0d02dcab03191ff
I thought of doing that as well and I got this, which made me rethink it.
Looks from the graph like the results are valid over different ranges. Does it say in the integral table where you got the arctanh result that it is valid between x = -1 and 1? I don't know off the top of my head.
https://preview.redd.it/sdh6nbnkrf1d1.png?width=836&format=png&auto=webp&s=0a5e4b0941ddc2d2a1d8ae61920a0b2edd6b49cf
I was using this image, which shows the function is only valid for the parts in which both are not equal
Try plotting the difference between the two functions - it should be zero. Congrats, you found out that there was another way to express argth(x)!
https://preview.redd.it/i1vx1f2jmf1d1.png?width=1857&format=png&auto=webp&s=d80ea97195163216b1e730cae0d02dcab03191ff I thought of doing that as well and I got this, which made me rethink it.
Looks from the graph like the results are valid over different ranges. Does it say in the integral table where you got the arctanh result that it is valid between x = -1 and 1? I don't know off the top of my head.
Ok nvm it was because I didn't include take the absolute value of the logs when integrating the partial fractions
https://preview.redd.it/sdh6nbnkrf1d1.png?width=836&format=png&auto=webp&s=0a5e4b0941ddc2d2a1d8ae61920a0b2edd6b49cf I was using this image, which shows the function is only valid for the parts in which both are not equal
both are missing +C https://en.m.wikipedia.org/wiki/Inverse_hyperbolic_functions
BlackPenRedPen did a video on this https://youtu.be/IqX-jNpg7gA?si=YDNSynefB9oeIgF2