8.1 Problem number 1054

$$\int x^{-1+14n}{(b+c{x}^n)}^{13}(b+2c{x}^n)dx$$

Optimal antiderivative $$\frac{x^{14n}{(b+c{x}^n)}^{14}}{14n}$$

command

integrate(x^(-1+14*n)*(b+c*x^n)^13*(b+2*c*x^n),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

$$\text{could not integrate}$$

Giac 1.7.0 via sagemath 9.3 output

$$\frac{c^{14}{x}^{28n}+14b{c}^{13}{x}^{27n}+91b^2{c}^{12}{x}^{26n}+364b^3{c}^{11}{x}^{25n}+1001b^4{c}^{10}{x}^{24n}+2002b^5{c}^9{x}^{23n}+3003b^6{c}^8{x}^{22n}+3432b^7{c}^7{x}^{21n}+3003b^8{c}^6{x}^{20n}+2002b^9{c}^5{x}^{19n}+1001b^{10}{c}^4{x}^{18n}+364b^{11}{c}^3{x}^{17n}+91b^{12}{c}^2{x}^{16n}+14b^{13}c{x}^{15n}+b^{14}{x}^{14n}}{14n}$$