\[ \int \sqrt {1+\sqrt {1+\sqrt {1+\sqrt {x}}}} \, dx \]
Optimal antiderivative \[ -\frac {32 \left (1+\sqrt {1+\sqrt {1+\sqrt {x}}}\right )^{\frac {5}{2}}}{5}+\frac {48 \left (1+\sqrt {1+\sqrt {1+\sqrt {x}}}\right )^{\frac {7}{2}}}{7}+\frac {112 \left (1+\sqrt {1+\sqrt {1+\sqrt {x}}}\right )^{\frac {9}{2}}}{9}-\frac {320 \left (1+\sqrt {1+\sqrt {1+\sqrt {x}}}\right )^{\frac {11}{2}}}{11}+\frac {288 \left (1+\sqrt {1+\sqrt {1+\sqrt {x}}}\right )^{\frac {13}{2}}}{13}-\frac {112 \left (1+\sqrt {1+\sqrt {1+\sqrt {x}}}\right )^{\frac {15}{2}}}{15}+\frac {16 \left (1+\sqrt {1+\sqrt {1+\sqrt {x}}}\right )^{\frac {17}{2}}}{17} \]
command
integrate((1+(1+(1+x^(1/2))^(1/2))^(1/2))^(1/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________