Optimal. Leaf size=213 \[ -\frac {\left (\sqrt {\sqrt {x+1}+1}+1\right )^{5/2}}{2 \left (\sqrt {x+1}-1\right ) \sqrt {\sqrt {x+1}+1}}+\frac {5 \sqrt {\sqrt {\sqrt {x+1}+1}+1}}{2 \left (\sqrt {x+1}-1\right ) \sqrt {\sqrt {x+1}+1}}-\frac {1}{4} \sqrt {17+25 \sqrt {2}} \tan ^{-1}\left (\frac {\sqrt {\sqrt {\sqrt {x+1}+1}+1}}{\sqrt {\sqrt {2}-1}}\right )+\tanh ^{-1}\left (\sqrt {\sqrt {\sqrt {x+1}+1}+1}\right )-\frac {1}{4} \sqrt {25 \sqrt {2}-17} \tanh ^{-1}\left (\frac {\sqrt {\sqrt {\sqrt {x+1}+1}+1}}{\sqrt {1+\sqrt {2}}}\right ) \]
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Rubi [B] time = 3.40, antiderivative size = 432, normalized size of antiderivative = 2.03, number of steps used = 19, number of rules used = 9, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.209, Rules used = {1586, 2102, 1594, 28, 2073, 207, 1178, 1166, 203} \begin {gather*} \frac {8 \left (\sqrt {\sqrt {x+1}+1}+1\right )^{3/2}}{3 \left (1-\sqrt {x+1}\right ) \sqrt {\sqrt {x+1}+1}}-\frac {\left (50-17 \sqrt {\sqrt {x+1}+1}\right ) \sqrt {\sqrt {\sqrt {x+1}+1}+1}}{30 \left (1-\sqrt {x+1}\right )}-\frac {24 \sqrt {\sqrt {\sqrt {x+1}+1}+1}}{5 \left (1-\sqrt {x+1}\right ) \sqrt {\sqrt {x+1}+1}}-\frac {1}{30 \left (1-\sqrt {\sqrt {\sqrt {x+1}+1}+1}\right )}+\frac {1}{30 \left (\sqrt {\sqrt {\sqrt {x+1}+1}+1}+1\right )}-\frac {1}{60} \sqrt {10961+8989 \sqrt {2}} \tan ^{-1}\left (\frac {\sqrt {\sqrt {\sqrt {x+1}+1}+1}}{\sqrt {\sqrt {2}-1}}\right )+\frac {1}{15} \sqrt {\frac {1}{2} \left (97+113 \sqrt {2}\right )} \tan ^{-1}\left (\frac {\sqrt {\sqrt {\sqrt {x+1}+1}+1}}{\sqrt {\sqrt {2}-1}}\right )+\tanh ^{-1}\left (\sqrt {\sqrt {\sqrt {x+1}+1}+1}\right )-\frac {1}{60} \sqrt {8989 \sqrt {2}-10961} \tanh ^{-1}\left (\frac {\sqrt {\sqrt {\sqrt {x+1}+1}+1}}{\sqrt {1+\sqrt {2}}}\right )-\frac {1}{15} \sqrt {\frac {1}{2} \left (113 \sqrt {2}-97\right )} \tanh ^{-1}\left (\frac {\sqrt {\sqrt {\sqrt {x+1}+1}+1}}{\sqrt {1+\sqrt {2}}}\right ) \end {gather*}
Warning: Unable to verify antiderivative.
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Rule 28
Rule 203
Rule 207
Rule 1166
Rule 1178
Rule 1586
Rule 1594
Rule 2073
Rule 2102
Rubi steps
\begin {align*} \int \frac {\sqrt {1+x} \sqrt {1+\sqrt {1+x}}}{x^2 \sqrt {1+\sqrt {1+\sqrt {1+x}}}} \, dx &=2 \operatorname {Subst}\left (\int \frac {x^2 \sqrt {1+x}}{\left (-1+x^2\right )^2 \sqrt {1+\sqrt {1+x}}} \, dx,x,\sqrt {1+x}\right )\\ &=2 \operatorname {Subst}\left (\int \frac {x^2}{(-1+x)^2 (1+x)^{3/2} \sqrt {1+\sqrt {1+x}}} \, dx,x,\sqrt {1+x}\right )\\ &=4 \operatorname {Subst}\left (\int \frac {\left (-1+x^2\right )^2}{x^2 \sqrt {1+x} \left (-2+x^2\right )^2} \, dx,x,\sqrt {1+\sqrt {1+x}}\right )\\ &=4 \operatorname {Subst}\left (\int \frac {(-1+x)^2 (1+x)^{3/2}}{x^2 \left (-2+x^2\right )^2} \, dx,x,\sqrt {1+\sqrt {1+x}}\right )\\ &=8 \operatorname {Subst}\left (\int \frac {x^4 \left (-2+x^2\right )^2}{\left (1+x^2-3 x^4+x^6\right )^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )\\ &=-\frac {8 \left (1+\sqrt {1+\sqrt {1+x}}\right )^{3/2}}{3 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {8}{3} \operatorname {Subst}\left (\int \frac {-3 x^2-13 x^4+9 x^6}{\left (1+x^2-3 x^4+x^6\right )^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )\\ &=-\frac {8 \left (1+\sqrt {1+\sqrt {1+x}}\right )^{3/2}}{3 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {8}{3} \operatorname {Subst}\left (\int \frac {x^2 \left (-3-13 x^2+9 x^4\right )}{\left (1+x^2-3 x^4+x^6\right )^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )\\ &=\frac {24 \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{5 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {8 \left (1+\sqrt {1+\sqrt {1+x}}\right )^{3/2}}{3 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}+\frac {8}{15} \operatorname {Subst}\left (\int \frac {-9+24 x^2-16 x^4}{\left (1+x^2-3 x^4+x^6\right )^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )\\ &=\frac {24 \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{5 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {8 \left (1+\sqrt {1+\sqrt {1+x}}\right )^{3/2}}{3 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {1}{30} \operatorname {Subst}\left (\int \frac {\left (12-16 x^2\right )^2}{\left (1+x^2-3 x^4+x^6\right )^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )\\ &=\frac {24 \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{5 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {8 \left (1+\sqrt {1+\sqrt {1+x}}\right )^{3/2}}{3 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {1}{30} \operatorname {Subst}\left (\int \left (\frac {1}{(-1+x)^2}+\frac {1}{(1+x)^2}+\frac {30}{-1+x^2}+\frac {8 \left (25+8 x^2\right )}{\left (-1-2 x^2+x^4\right )^2}-\frac {4 \left (-7+8 x^2\right )}{-1-2 x^2+x^4}\right ) \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )\\ &=-\frac {1}{30 \left (1-\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )}+\frac {1}{30 \left (1+\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )}+\frac {24 \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{5 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {8 \left (1+\sqrt {1+\sqrt {1+x}}\right )^{3/2}}{3 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}+\frac {2}{15} \operatorname {Subst}\left (\int \frac {-7+8 x^2}{-1-2 x^2+x^4} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )-\frac {4}{15} \operatorname {Subst}\left (\int \frac {25+8 x^2}{\left (-1-2 x^2+x^4\right )^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )-\operatorname {Subst}\left (\int \frac {1}{-1+x^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )\\ &=-\frac {1}{30 \left (1-\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )}+\frac {1}{30 \left (1+\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )}-\frac {\left (50-17 \sqrt {1+\sqrt {1+x}}\right ) \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{30 \left (1+2 \left (1+\sqrt {1+\sqrt {1+x}}\right )-\left (1+\sqrt {1+\sqrt {1+x}}\right )^2\right )}+\frac {24 \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{5 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {8 \left (1+\sqrt {1+\sqrt {1+x}}\right )^{3/2}}{3 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}+\tanh ^{-1}\left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )-\frac {1}{60} \operatorname {Subst}\left (\int \frac {-266+34 x^2}{-1-2 x^2+x^4} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )+\frac {1}{30} \left (16-\sqrt {2}\right ) \operatorname {Subst}\left (\int \frac {1}{-1+\sqrt {2}+x^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )+\frac {1}{30} \left (16+\sqrt {2}\right ) \operatorname {Subst}\left (\int \frac {1}{-1-\sqrt {2}+x^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )\\ &=-\frac {1}{30 \left (1-\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )}+\frac {1}{30 \left (1+\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )}-\frac {\left (50-17 \sqrt {1+\sqrt {1+x}}\right ) \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{30 \left (1+2 \left (1+\sqrt {1+\sqrt {1+x}}\right )-\left (1+\sqrt {1+\sqrt {1+x}}\right )^2\right )}+\frac {24 \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{5 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {8 \left (1+\sqrt {1+\sqrt {1+x}}\right )^{3/2}}{3 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}+\frac {1}{30} \sqrt {194+226 \sqrt {2}} \tan ^{-1}\left (\frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{\sqrt {-1+\sqrt {2}}}\right )+\tanh ^{-1}\left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )-\frac {1}{30} \sqrt {-194+226 \sqrt {2}} \tanh ^{-1}\left (\frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{\sqrt {1+\sqrt {2}}}\right )-\frac {1}{60} \left (17-58 \sqrt {2}\right ) \operatorname {Subst}\left (\int \frac {1}{-1-\sqrt {2}+x^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )-\frac {1}{60} \left (17+58 \sqrt {2}\right ) \operatorname {Subst}\left (\int \frac {1}{-1+\sqrt {2}+x^2} \, dx,x,\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )\\ &=-\frac {1}{30 \left (1-\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )}+\frac {1}{30 \left (1+\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )}-\frac {\left (50-17 \sqrt {1+\sqrt {1+x}}\right ) \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{30 \left (1+2 \left (1+\sqrt {1+\sqrt {1+x}}\right )-\left (1+\sqrt {1+\sqrt {1+x}}\right )^2\right )}+\frac {24 \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{5 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}-\frac {8 \left (1+\sqrt {1+\sqrt {1+x}}\right )^{3/2}}{3 \left (2+\sqrt {1+\sqrt {1+x}}-3 \left (1+\sqrt {1+\sqrt {1+x}}\right )^2+\left (1+\sqrt {1+\sqrt {1+x}}\right )^3\right )}+\frac {1}{30} \sqrt {194+226 \sqrt {2}} \tan ^{-1}\left (\frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{\sqrt {-1+\sqrt {2}}}\right )-\frac {1}{60} \sqrt {10961+8989 \sqrt {2}} \tan ^{-1}\left (\frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{\sqrt {-1+\sqrt {2}}}\right )+\tanh ^{-1}\left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )-\frac {1}{30} \sqrt {-194+226 \sqrt {2}} \tanh ^{-1}\left (\frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{\sqrt {1+\sqrt {2}}}\right )-\frac {1}{60} \sqrt {-10961+8989 \sqrt {2}} \tanh ^{-1}\left (\frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{\sqrt {1+\sqrt {2}}}\right )\\ \end {align*}
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Mathematica [A] time = 1.04, size = 357, normalized size = 1.68 \begin {gather*} \frac {1}{4} \left (\frac {\left (\sqrt {2}-1\right ) \sqrt {\sqrt {\sqrt {x+1}+1}+1}}{\sqrt {2}-\sqrt {\sqrt {x+1}+1}}+\frac {\left (1+\sqrt {2}\right ) \sqrt {\sqrt {\sqrt {x+1}+1}+1}}{\sqrt {\sqrt {x+1}+1}+\sqrt {2}}-\frac {2}{\sqrt {\sqrt {\sqrt {x+1}+1}+1}-1}-\frac {2}{\sqrt {\sqrt {\sqrt {x+1}+1}+1}+1}-5 \sqrt {2 \left (1+\sqrt {2}\right )} \tan ^{-1}\left (\sqrt {1+\sqrt {2}} \sqrt {\sqrt {\sqrt {x+1}+1}+1}\right )+\frac {\tan ^{-1}\left (\sqrt {1+\sqrt {2}} \sqrt {\sqrt {\sqrt {x+1}+1}+1}\right )}{\left (\sqrt {2}-1\right )^{3/2}}+4 \tanh ^{-1}\left (\sqrt {\sqrt {\sqrt {x+1}+1}+1}\right )+\frac {\tanh ^{-1}\left (\sqrt {\sqrt {2}-1} \sqrt {\sqrt {\sqrt {x+1}+1}+1}\right )}{\left (1+\sqrt {2}\right )^{3/2}}-5 \sqrt {2 \left (\sqrt {2}-1\right )} \tanh ^{-1}\left (\sqrt {\sqrt {2}-1} \sqrt {\sqrt {\sqrt {x+1}+1}+1}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.94, size = 210, normalized size = 0.99 \begin {gather*} \frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{1-\sqrt {1+x}}+\frac {\left (3-\sqrt {1+x}\right ) \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{2 \left (-1+\sqrt {1+x}\right ) \sqrt {1+\sqrt {1+x}}}-\frac {1}{4} \sqrt {17+25 \sqrt {2}} \tan ^{-1}\left (\sqrt {1+\sqrt {2}} \sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )+\tanh ^{-1}\left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}\right )-\frac {1}{4} \sqrt {-17+25 \sqrt {2}} \tanh ^{-1}\left (\sqrt {-1+\sqrt {2}} \sqrt {1+\sqrt {1+\sqrt {1+x}}}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 255, normalized size = 1.20 \begin {gather*} \frac {4 \, x \sqrt {25 \, \sqrt {2} + 17} \arctan \left (\frac {1}{31} \, \sqrt {25 \, \sqrt {2} + 17} {\left (4 \, \sqrt {2} + 1\right )} \sqrt {\sqrt {2} + \sqrt {\sqrt {x + 1} + 1}} - \frac {1}{31} \, \sqrt {25 \, \sqrt {2} + 17} {\left (4 \, \sqrt {2} + 1\right )} \sqrt {\sqrt {\sqrt {x + 1} + 1} + 1}\right ) - x \sqrt {25 \, \sqrt {2} - 17} \log \left (\sqrt {25 \, \sqrt {2} - 17} {\left (3 \, \sqrt {2} + 7\right )} + 31 \, \sqrt {\sqrt {\sqrt {x + 1} + 1} + 1}\right ) + x \sqrt {25 \, \sqrt {2} - 17} \log \left (-\sqrt {25 \, \sqrt {2} - 17} {\left (3 \, \sqrt {2} + 7\right )} + 31 \, \sqrt {\sqrt {\sqrt {x + 1} + 1} + 1}\right ) + 4 \, x \log \left (\sqrt {\sqrt {\sqrt {x + 1} + 1} + 1} + 1\right ) - 4 \, x \log \left (\sqrt {\sqrt {\sqrt {x + 1} + 1} + 1} - 1\right ) - 4 \, {\left (\sqrt {\sqrt {x + 1} + 1} {\left (\sqrt {x + 1} - 3\right )} + 2 \, \sqrt {x + 1} + 2\right )} \sqrt {\sqrt {\sqrt {x + 1} + 1} + 1}}{8 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.26, size = 215, normalized size = 1.01
method | result | size |
derivativedivides | \(-\frac {1}{2 \left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}-1\right )}-\frac {\ln \left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}-1\right )}{2}-\frac {1}{2 \left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}+1\right )}+\frac {\ln \left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}+1\right )}{2}+\frac {\frac {\left (1+\sqrt {1+\sqrt {1+x}}\right )^{\frac {3}{2}}}{2}-\frac {3 \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{2}}{\left (1+\sqrt {1+\sqrt {1+x}}\right )^{2}-2 \sqrt {1+\sqrt {1+x}}-3}-\frac {\left (8+\sqrt {2}\right ) \sqrt {2}\, \arctanh \left (\frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{\sqrt {1+\sqrt {2}}}\right )}{8 \sqrt {1+\sqrt {2}}}+\frac {\left (-8+\sqrt {2}\right ) \sqrt {2}\, \arctan \left (\frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{\sqrt {\sqrt {2}-1}}\right )}{8 \sqrt {\sqrt {2}-1}}\) | \(215\) |
default | \(-\frac {1}{2 \left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}-1\right )}-\frac {\ln \left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}-1\right )}{2}-\frac {1}{2 \left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}+1\right )}+\frac {\ln \left (\sqrt {1+\sqrt {1+\sqrt {1+x}}}+1\right )}{2}+\frac {\frac {\left (1+\sqrt {1+\sqrt {1+x}}\right )^{\frac {3}{2}}}{2}-\frac {3 \sqrt {1+\sqrt {1+\sqrt {1+x}}}}{2}}{\left (1+\sqrt {1+\sqrt {1+x}}\right )^{2}-2 \sqrt {1+\sqrt {1+x}}-3}-\frac {\left (8+\sqrt {2}\right ) \sqrt {2}\, \arctanh \left (\frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{\sqrt {1+\sqrt {2}}}\right )}{8 \sqrt {1+\sqrt {2}}}+\frac {\left (-8+\sqrt {2}\right ) \sqrt {2}\, \arctan \left (\frac {\sqrt {1+\sqrt {1+\sqrt {1+x}}}}{\sqrt {\sqrt {2}-1}}\right )}{8 \sqrt {\sqrt {2}-1}}\) | \(215\) |
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 {\sqrt {x + 1} \sqrt {\sqrt {x + 1} + 1}}{x^{2} \sqrt {\sqrt {\sqrt {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 {\sqrt {\sqrt {x+1}+1}\,\sqrt {x+1}}{x^2\,\sqrt {\sqrt {\sqrt {x+1}+1}+1}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [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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