13.3 Problem number 1760

$$\int {(a+\frac{b}{x})}^{3/2}{x}^{9/2}dx$$

Optimal antiderivative $$-\frac{32b^3{(a+\frac{b}{x})}^{\frac{5}{2}}{x}^{\frac{5}{2}}}{1155a^4}+\frac{16b^2{(a+\frac{b}{x})}^{\frac{5}{2}}{x}^{\frac{7}{2}}}{231a^3}-\frac{4b{(a+\frac{b}{x})}^{\frac{5}{2}}{x}^{\frac{9}{2}}}{33a^2}+\frac{2{(a+\frac{b}{x})}^{\frac{5}{2}}{x}^{\frac{11}{2}}}{11a}$$

command

integrate((a+b/x)**(3/2)*x**(9/2),x)

Sympy 1.10.1 under Python 3.10.4 output

$$\text{Exception raised: SystemError}$$

Sympy 1.8 under Python 3.8.8 output

$$\frac{210a^8{b}^{\frac{19}{2}}{x}^8\sqrt{\frac{ax}{b}+1}}{1155a^7{b}^9{x}^3+3465a^6{b}^{10}{x}^2+3465a^5{b}^{11}x+1155a^4{b}^{12}}+\frac{910a^7{b}^{\frac{21}{2}}{x}^7\sqrt{\frac{ax}{b}+1}}{1155a^7{b}^9{x}^3+3465a^6{b}^{10}{x}^2+3465a^5{b}^{11}x+1155a^4{b}^{12}}+\frac{1480a^6{b}^{\frac{23}{2}}{x}^6\sqrt{\frac{ax}{b}+1}}{1155a^7{b}^9{x}^3+3465a^6{b}^{10}{x}^2+3465a^5{b}^{11}x+1155a^4{b}^{12}}+\frac{1068a^5{b}^{\frac{25}{2}}{x}^5\sqrt{\frac{ax}{b}+1}}{1155a^7{b}^9{x}^3+3465a^6{b}^{10}{x}^2+3465a^5{b}^{11}x+1155a^4{b}^{12}}+\frac{290a^4{b}^{\frac{27}{2}}{x}^4\sqrt{\frac{ax}{b}+1}}{1155a^7{b}^9{x}^3+3465a^6{b}^{10}{x}^2+3465a^5{b}^{11}x+1155a^4{b}^{12}}-\frac{10a^3{b}^{\frac{29}{2}}{x}^3\sqrt{\frac{ax}{b}+1}}{1155a^7{b}^9{x}^3+3465a^6{b}^{10}{x}^2+3465a^5{b}^{11}x+1155a^4{b}^{12}}-\frac{60a^2{b}^{\frac{31}{2}}{x}^2\sqrt{\frac{ax}{b}+1}}{1155a^7{b}^9{x}^3+3465a^6{b}^{10}{x}^2+3465a^5{b}^{11}x+1155a^4{b}^{12}}-\frac{80a{b}^{\frac{33}{2}}x\sqrt{\frac{ax}{b}+1}}{1155a^7{b}^9{x}^3+3465a^6{b}^{10}{x}^2+3465a^5{b}^{11}x+1155a^4{b}^{12}}-\frac{32b^{\frac{35}{2}}\sqrt{\frac{ax}{b}+1}}{1155a^7{b}^9{x}^3+3465a^6{b}^{10}{x}^2+3465a^5{b}^{11}x+1155a^4{b}^{12}}$$