The following question remain open and requests further research given function hypothesis.


Is it possible to obtain a closed expression to the inverse of a function integral.


$\int\_{0}^t \frac{1}{f(\tau)} d \tau = g(t) - g(0)$


Above the corresponding function is g(t). I thank in advance.



Integral of inverse of a function
Take $f(\tau):=\dfrac{1}{e^{-\tau^2}}$, the integral you get can not be expressed by means of usual functions. You can just get an expression with the error function $\mathrm{erf}$.


