$$\int \Gamma(x)^{dx}=C \frac{e^{\psi^{(-2)}(x)}}{\Gamma(x)}$$e^{\psi^{(-2)}(x)}$$if to use the popular generalization of polygamma function \psi^{(p)}(z) put forward by Grossman in 1976. If to use a more modern "balanced" generalization \psi(p,x) by Espinoza and Moll of 2004, the integral will be as follows:$$\int \Gamma(x)^{dx}=C e^{\psi(-2,x)-\frac e^{\psi(-2,x)+\frac {x}{2}\ln 2\pi}$$2 deleted 1 characters in body Multiplicative integral of gamma function is$$\int \Gamma(x)^{dx}=C \frac{e^{\psi^{(-2)}(x)}}{\Gamma(x)}$$if to use the popular generalization of polygamma function \psi^{(p)}(z) put forward by Groissman Grossman in 1976. If to use a more modern "balanced" generalization \psi(p,x) by Espinoza and Moll of 2004, the integral will be as follows:$$\int \Gamma(x)^{dx}=C e^{\psi(-2,x)-\frac {x}{2}\ln 2\pi}$$1 Multiplicative integral of gamma function is$$\int \Gamma(x)^{dx}=C \frac{e^{\psi^{(-2)}(x)}}{\Gamma(x)}$$if to use the popular generalization of polygamma function \psi^{(p)}(z) put forward by Groissman in 1976. If to use a more modern "balanced" generalization \psi(p,x) by Espinoza and Moll of 2004, the integral will be as follows:$$\int \Gamma(x)^{dx}=C e^{\psi(-2,x)-\frac {x}{2}\ln 2\pi}