I solve an easy example to check that Mathematica can understand the difference between ArcTan and ArcTanh but as you see here I can't get Arctanh??!! Even I don't know why the inverse function is not working! thanks for helping
g = Integrate[1/((-(3/2))*x^2 + (3/2)*a*x+ b/2), x, Assumptions -> {a > 0, b > 0}]
Assuming[{a > 0, b >0},InverseFunction[g][x]]
a,b are positive.
g
isn't a function; it's a symbolic expression. Tryg[x_] = Integrate[...]
instead (afterClear[g]
); $\endgroup$