Optimal. Leaf size=501 \[ \frac {-291 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^{15/2}+2275 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^{13/2}-6611 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^{11/2}+8403 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^{9/2}-3301 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^{7/2}-2139 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^{5/2}+1787 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^{3/2}+69 \sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{384 \left (\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2-2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-1\right )^2 \left (1-\sqrt {1-\frac {1}{x}}\right )^2}+\left (-\frac {19}{64} \sqrt {\frac {1}{2} \left (\frac {1}{2}+\frac {1}{\sqrt {2}}\right )}-\frac {11}{64} \sqrt {\frac {1}{2}+\frac {1}{\sqrt {2}}}\right ) \tan ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {\sqrt {2}-1}}\right )+\frac {59}{128} \tanh ^{-1}\left (\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )+\left (\frac {19}{64} \sqrt {\frac {1}{2} \left (\frac {1}{\sqrt {2}}-\frac {1}{2}\right )}-\frac {11}{64} \sqrt {\frac {1}{\sqrt {2}}-\frac {1}{2}}\right ) \tanh ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {1+\sqrt {2}}}\right ) \]
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Rubi [A] time = 1.50, antiderivative size = 758, normalized size of antiderivative = 1.51, number of steps used = 16, number of rules used = 6, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.207, Rules used = {1586, 1692, 207, 1178, 1166, 203} \begin {gather*} -\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (\sqrt {1-\sqrt {1-\frac {1}{x}}}+1\right )}{8 \left (\sqrt {1-\frac {1}{x}}+1\right )}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (\sqrt {1-\sqrt {1-\frac {1}{x}}}+1\right )}{8 \left (\sqrt {1-\frac {1}{x}}+1\right )^2}+\frac {59}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {59}{256 \left (\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}+1\right )}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (11 \sqrt {1-\sqrt {1-\frac {1}{x}}}+12\right )}{64 \left (\sqrt {1-\frac {1}{x}}+1\right )}+\frac {23}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}-\frac {23}{256 \left (\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}+1\right )^2}+\frac {5}{192 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}-\frac {5}{192 \left (\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}+1\right )^3}+\frac {1}{128 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}-\frac {1}{128 \left (\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}+1\right )^4}-\frac {1}{128} \sqrt {527+373 \sqrt {2}} \tan ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {\sqrt {2}-1}}\right )-\frac {\left (1+\sqrt {2}\right )^{3/2} \tan ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {\sqrt {2}-1}}\right )}{16 \sqrt {2}}+\frac {59}{128} \tanh ^{-1}\left (\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )+\frac {1}{128} \sqrt {373 \sqrt {2}-527} \tanh ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {1+\sqrt {2}}}\right )+\frac {\left (\sqrt {2}-1\right )^{3/2} \tanh ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {1+\sqrt {2}}}\right )}{16 \sqrt {2}} \end {gather*}
Warning: Unable to verify antiderivative.
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Rule 203
Rule 207
Rule 1166
Rule 1178
Rule 1586
Rule 1692
Rubi steps
\begin {align*} \int \frac {x}{\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}} \, dx &=-\left (2 \operatorname {Subst}\left (\int \frac {x}{\sqrt {1-\sqrt {1-x}} \left (-1+x^2\right )^3} \, dx,x,\sqrt {1-\frac {1}{x}}\right )\right )\\ &=4 \operatorname {Subst}\left (\int \frac {1-x^2}{\sqrt {1-x} x^5 \left (-2+x^2\right )^3} \, dx,x,\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )\\ &=4 \operatorname {Subst}\left (\int \frac {\sqrt {1-x} (1+x)}{x^5 \left (-2+x^2\right )^3} \, dx,x,\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )\\ &=-\left (8 \operatorname {Subst}\left (\int \frac {x^2 \left (-2+x^2\right )}{\left (-1+x^2\right )^5 \left (-1-2 x^2+x^4\right )^3} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )\right )\\ &=-\left (8 \operatorname {Subst}\left (\int \left (\frac {1}{256 (-1+x)^5}-\frac {5}{512 (-1+x)^4}+\frac {23}{1024 (-1+x)^3}-\frac {59}{2048 (-1+x)^2}-\frac {1}{256 (1+x)^5}-\frac {5}{512 (1+x)^4}-\frac {23}{1024 (1+x)^3}-\frac {59}{2048 (1+x)^2}+\frac {59}{1024 \left (-1+x^2\right )}+\frac {-1+x^2}{8 \left (-1-2 x^2+x^4\right )^3}+\frac {1-x^2}{16 \left (-1-2 x^2+x^4\right )^2}\right ) \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )\right )\\ &=\frac {1}{128 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}+\frac {5}{192 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}+\frac {23}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}+\frac {59}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {1}{128 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}-\frac {5}{192 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}-\frac {23}{256 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}-\frac {59}{256 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {59}{128} \operatorname {Subst}\left (\int \frac {1}{-1+x^2} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )-\frac {1}{2} \operatorname {Subst}\left (\int \frac {1-x^2}{\left (-1-2 x^2+x^4\right )^2} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )-\operatorname {Subst}\left (\int \frac {-1+x^2}{\left (-1-2 x^2+x^4\right )^3} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )\\ &=\frac {1}{128 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}+\frac {5}{192 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}+\frac {23}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}+\frac {59}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {1}{128 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}-\frac {5}{192 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}-\frac {23}{256 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}-\frac {59}{256 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (1+\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )}{8 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )^2}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (1+\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )}{8 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )}+\frac {59}{128} \tanh ^{-1}\left (\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )-\frac {1}{32} \operatorname {Subst}\left (\int \frac {24-20 x^2}{\left (-1-2 x^2+x^4\right )^2} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )-\frac {1}{32} \operatorname {Subst}\left (\int \frac {-8+4 x^2}{-1-2 x^2+x^4} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )\\ &=\frac {1}{128 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}+\frac {5}{192 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}+\frac {23}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}+\frac {59}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {1}{128 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}-\frac {5}{192 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}-\frac {23}{256 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}-\frac {59}{256 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (1+\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )}{8 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )^2}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (1+\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )}{8 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (12+11 \sqrt {1-\sqrt {-\frac {1-x}{x}}}\right )}{64 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )}+\frac {59}{128} \tanh ^{-1}\left (\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )-\frac {1}{512} \operatorname {Subst}\left (\int \frac {-200+88 x^2}{-1-2 x^2+x^4} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )-\frac {1}{32} \left (2-\sqrt {2}\right ) \operatorname {Subst}\left (\int \frac {1}{-1-\sqrt {2}+x^2} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )-\frac {1}{32} \left (2+\sqrt {2}\right ) \operatorname {Subst}\left (\int \frac {1}{-1+\sqrt {2}+x^2} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )\\ &=\frac {1}{128 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}+\frac {5}{192 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}+\frac {23}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}+\frac {59}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {1}{128 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}-\frac {5}{192 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}-\frac {23}{256 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}-\frac {59}{256 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (1+\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )}{8 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )^2}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (1+\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )}{8 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (12+11 \sqrt {1-\sqrt {-\frac {1-x}{x}}}\right )}{64 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )}-\frac {\left (1+\sqrt {2}\right )^{3/2} \tan ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {-1+\sqrt {2}}}\right )}{16 \sqrt {2}}+\frac {59}{128} \tanh ^{-1}\left (\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )+\frac {\left (-1+\sqrt {2}\right )^{3/2} \tanh ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {1+\sqrt {2}}}\right )}{16 \sqrt {2}}-\frac {1}{128} \left (11-7 \sqrt {2}\right ) \operatorname {Subst}\left (\int \frac {1}{-1-\sqrt {2}+x^2} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )-\frac {1}{128} \left (11+7 \sqrt {2}\right ) \operatorname {Subst}\left (\int \frac {1}{-1+\sqrt {2}+x^2} \, dx,x,\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )\\ &=\frac {1}{128 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}+\frac {5}{192 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}+\frac {23}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}+\frac {59}{256 \left (1-\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {1}{128 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^4}-\frac {5}{192 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^3}-\frac {23}{256 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )^2}-\frac {59}{256 \left (1+\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (1+\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )}{8 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )^2}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (1+\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )}{8 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )}-\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}} \left (12+11 \sqrt {1-\sqrt {-\frac {1-x}{x}}}\right )}{64 \left (1+2 \left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )-\left (1-\sqrt {1-\sqrt {1-\frac {1}{x}}}\right )^2\right )}-\frac {\left (1+\sqrt {2}\right )^{3/2} \tan ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {-1+\sqrt {2}}}\right )}{16 \sqrt {2}}-\frac {1}{128} \sqrt {527+373 \sqrt {2}} \tan ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {-1+\sqrt {2}}}\right )+\frac {59}{128} \tanh ^{-1}\left (\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}\right )+\frac {\left (-1+\sqrt {2}\right )^{3/2} \tanh ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {1+\sqrt {2}}}\right )}{16 \sqrt {2}}+\frac {1}{128} \sqrt {-527+373 \sqrt {2}} \tanh ^{-1}\left (\frac {\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}{\sqrt {1+\sqrt {2}}}\right )\\ \end {align*}
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Mathematica [A] time = 1.40, size = 467, normalized size = 0.93 \begin {gather*} \frac {32 \sqrt {1-\sqrt {\frac {x-1}{x}}} x^2+32 \sqrt {1-\sqrt {\frac {x-1}{x}}} \sqrt {\frac {x-1}{x}} x^2+384 x^2+114 \sqrt {1-\sqrt {\frac {x-1}{x}}} x+106 \sqrt {1-\sqrt {\frac {x-1}{x}}} \sqrt {\frac {x-1}{x}} x+4 \sqrt {\frac {x-1}{x}} x+52 x-177 \sqrt {1-\sqrt {1-\sqrt {\frac {x-1}{x}}}} \log \left (1-\frac {1}{\sqrt {1-\sqrt {1-\sqrt {\frac {x-1}{x}}}}}\right )+177 \sqrt {1-\sqrt {1-\sqrt {\frac {x-1}{x}}}} \log \left (\frac {1}{\sqrt {1-\sqrt {1-\sqrt {\frac {x-1}{x}}}}}+1\right )+6 \sqrt {\sqrt {2}-1} \left (41+30 \sqrt {2}\right ) \sqrt {1-\sqrt {1-\sqrt {\frac {x-1}{x}}}} \tan ^{-1}\left (\frac {1}{\sqrt {1+\sqrt {2}} \sqrt {1-\sqrt {1-\sqrt {\frac {x-1}{x}}}}}\right )+6 \sqrt {1+\sqrt {2}} \left (30 \sqrt {2}-41\right ) \sqrt {1-\sqrt {1-\sqrt {\frac {x-1}{x}}}} \tanh ^{-1}\left (\frac {1}{\sqrt {\sqrt {2}-1} \sqrt {1-\sqrt {1-\sqrt {\frac {x-1}{x}}}}}\right )-582}{768 \sqrt {1-\sqrt {1-\sqrt {\frac {x-1}{x}}}}} \end {gather*}
Warning: Unable to verify antiderivative.
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IntegrateAlgebraic [F] time = 3.70, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.45, size = 344, normalized size = 0.69 \begin {gather*} \frac {1}{384} \, {\left ({\left (16 \, x^{2} + {\left (208 \, x^{2} + 291 \, x\right )} \sqrt {\frac {x - 1}{x}} + 55 \, x\right )} \sqrt {-\sqrt {\frac {x - 1}{x}} + 1} + 2 \, {\left (96 \, x^{2} + 119 \, x\right )} \sqrt {\frac {x - 1}{x}} - 2 \, x\right )} \sqrt {-\sqrt {-\sqrt {\frac {x - 1}{x}} + 1} + 1} + \frac {1}{64} \, \sqrt {1021 \, \sqrt {2} + 1439} \arctan \left (-\frac {1}{119} \, \sqrt {1021 \, \sqrt {2} + 1439} {\left (11 \, \sqrt {2} - 19\right )} \sqrt {\sqrt {2} - \sqrt {-\sqrt {\frac {x - 1}{x}} + 1}} + \frac {1}{119} \, \sqrt {1021 \, \sqrt {2} + 1439} {\left (11 \, \sqrt {2} - 19\right )} \sqrt {-\sqrt {-\sqrt {\frac {x - 1}{x}} + 1} + 1}\right ) + \frac {1}{256} \, \sqrt {1021 \, \sqrt {2} - 1439} \log \left (\sqrt {1021 \, \sqrt {2} - 1439} {\left (30 \, \sqrt {2} + 41\right )} + 119 \, \sqrt {-\sqrt {-\sqrt {\frac {x - 1}{x}} + 1} + 1}\right ) - \frac {1}{256} \, \sqrt {1021 \, \sqrt {2} - 1439} \log \left (-\sqrt {1021 \, \sqrt {2} - 1439} {\left (30 \, \sqrt {2} + 41\right )} + 119 \, \sqrt {-\sqrt {-\sqrt {\frac {x - 1}{x}} + 1} + 1}\right ) + \frac {59}{256} \, \log \left (\sqrt {-\sqrt {-\sqrt {\frac {x - 1}{x}} + 1} + 1} + 1\right ) - \frac {59}{256} \, \log \left (\sqrt {-\sqrt {-\sqrt {\frac {x - 1}{x}} + 1} + 1} - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.20, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{\sqrt {-\sqrt {-\sqrt {-\frac {1}{x} + 1} + 1} + 1}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {x}{\sqrt {1-\sqrt {1-\sqrt {1-\frac {1}{x}}}}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{\sqrt {1 - \sqrt {1 - \sqrt {1 - \frac {1}{x}}}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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