3.30.5 \(\int \frac {(1+x^2) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)
Optimal. Leaf size=323 \[ \frac {1}{8} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+4 \text {$\#$1}^4-2\& ,\frac {3 \text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-4 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )+\log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^5-2 \text {$\#$1}^3}\& \right ]+\frac {1}{8} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+8 \text {$\#$1}^4-8 \text {$\#$1}^2+2\& ,\frac {3 \text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-4 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )+\log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^5-2 \text {$\#$1}^3+2 \text {$\#$1}}\& \right ]-\frac {\sqrt {\sqrt {x^2+1}+x} \sqrt {\sqrt {\sqrt {x^2+1}+x}+1} x}{x^2-1} \]
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Rubi [F] time = 3.45, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \int \frac {\left (1+x^2\right ) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]
[Out]
Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/2 + Defer[Int][(Sqrt[x +
Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/2
Rubi steps
\begin {align*} \int \frac {\left (1+x^2\right ) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2} \, dx &=\int \left (\frac {2 \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2}-\frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2}\right ) \, dx\\ &=2 \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2} \, dx-\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\\ &=2 \int \left (\frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{4 (1-x)^2}+\frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{4 (1+x)^2}+\frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 \left (1-x^2\right )}\right ) \, dx-\int \left (\frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 (1-x)}+\frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 (1+x)}\right ) \, dx\\ &=\frac {1}{2} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2} \, dx-\frac {1}{2} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x} \, dx+\frac {1}{2} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2} \, dx-\frac {1}{2} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1+x} \, dx+\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\\ &=\frac {1}{2} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2} \, dx-\frac {1}{2} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x} \, dx+\frac {1}{2} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2} \, dx-\frac {1}{2} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1+x} \, dx+\int \left (\frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 (1-x)}+\frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 (1+x)}\right ) \, dx\\ &=\frac {1}{2} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2} \, dx+\frac {1}{2} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2} \, dx\\ \end {align*}
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Mathematica [F] time = 7.47, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (1+x^2\right ) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Integrate[((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]
[Out]
Integrate[((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2, x]
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IntegrateAlgebraic [B] time = 0.77, size = 686, normalized size = 2.12 \begin {gather*} -\frac {x \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{-1+x^2}+\frac {1}{2} \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {3 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{2 \text {$\#$1}-3 \text {$\#$1}^3+\text {$\#$1}^5}\&\right ]-\frac {1}{8} \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )+7 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2-\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^6}{2 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]+\frac {1}{2} \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {-\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}-2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^3+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^5}{-2+4 \text {$\#$1}^2-3 \text {$\#$1}^4+\text {$\#$1}^6}\&\right ]-\frac {1}{8} \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-9 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2-\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^6}{-2 \text {$\#$1}+4 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ] \end {gather*}
Antiderivative was successfully verified.
[In]
IntegrateAlgebraic[((1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]
[Out]
-((x*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(-1 + x^2)) + RootSum[-2 + 4*#1^4 - 4*#1^6 + #
1^8 & , (3*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 +
Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1 - 3*#1^3 + #1^5) & ]/2 - RootSum[-2 + 4*#1^4 - 4*#1^6
+ #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] + 7*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 -
Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4 + Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^6)/(2*#1^3
- 3*#1^5 + #1^7) & ]/8 + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-(Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2
]]] - #1]*#1) - 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3 + Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #
1]*#1^5)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]/2 - RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + S
qrt[x + Sqrt[1 + x^2]]] - #1] - 9*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 - Log[Sqrt[1 + Sqrt[x + Sqr
t[1 + x^2]]] - #1]*#1^4 + Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^6)/(-2*#1 + 4*#1^3 - 3*#1^5 + #1^7) &
]/8
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fricas [B] time = 1.85, size = 6976, normalized size = 21.60
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm="fricas")
[Out]
1/16*(sqrt(2)*(x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 + 1/1
6*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) + 1
2) - 3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*
sqrt(2) + 673) - 5/2*sqrt(2) + 2)*log(1/8*(5*(300981*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2)
- 4) - 1111618*sqrt(2))*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 - 5558090*sqrt(2)*(2*sqrt(1/
2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - (1504905*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sq
rt(2) - 4)^2 + 24078480*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4) - 213263242*sqrt(2))*(2
*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4) + 8*(5*(601962*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 15049
05*sqrt(2) - 2315542)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4) + 11116180*sqrt(1/2)*sqrt(941*sqr
t(2) + 1321) - 27790450*sqrt(2) - 146566162)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)
^2 + 1/16*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqr
t(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(941*sqrt(2) + 13
21) + 5*sqrt(2) + 673) - 213263242*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4) - 5544442608
*sqrt(2))*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)
*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) + 12) - 3/32*(2*s
qrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 673)
- 5/2*sqrt(2) + 2) + 18101760817*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - sqrt(2)*(x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/
32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*s
qrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 132
1) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 673) - 5/2*sqrt(2) + 2)*log(-1/8*(5
*(300981*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4) - 1111618*sqrt(2))*(2*sqrt(1/2)*sqrt(9
41*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 - 5558090*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)
^2 - (1504905*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 + 24078480*sqrt(2)*(2*sqrt(1/2)
*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4) - 213263242*sqrt(2))*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt
(2) + 4) + 8*(5*(601962*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 1504905*sqrt(2) - 2315542)*(2*sqrt(1/2)*sqrt(941*
sqrt(2) + 1321) + 5*sqrt(2) + 4) + 11116180*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 27790450*sqrt(2) - 146566162)
*sqrt(-3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 13
21) + 5*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(941*sqrt
(2) + 1321) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 673) - 213263242*sqrt(2)*(
2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4) - 5544442608*sqrt(2))*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/
2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)*(
2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2
) - 4)^2 - 2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 673) - 5/2*sqrt(2) + 2) + 18101760817*sqrt(sqrt(
x + sqrt(x^2 + 1)) + 1)) + sqrt(2)*(x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) +
5*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*sqrt(2) +
1321) - 5*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(94
1*sqrt(2) + 1321) + 5*sqrt(2) + 673) - 5/2*sqrt(2) + 2)*log(1/8*(5*(300981*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(
2) + 1321) - 5*sqrt(2) - 4) - 1111618*sqrt(2))*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 - 5558
090*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - (1504905*sqrt(2)*(2*sqrt(1/2)*sqrt(941*
sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 + 24078480*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4) -
213263242*sqrt(2))*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4) - 8*(5*(601962*sqrt(1/2)*sqrt(941*s
qrt(2) + 1321) - 1504905*sqrt(2) - 2315542)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4) + 11116180*
sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 27790450*sqrt(2) - 146566162)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) +
1321) + 5*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*s
qrt(2) + 1321) - 5*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)
*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 673) - 213263242*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqr
t(2) - 4) - 5544442608*sqrt(2))*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4
)^2 + 1/16*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sq
rt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(941*sqrt(2) + 1
321) + 5*sqrt(2) + 673) - 5/2*sqrt(2) + 2) + 18101760817*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - sqrt(2)*(x^2 - 1
)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(9
41*sqrt(2) + 1321) + 5*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) + 12) - 3/32*(2*sqrt(1/2
)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 673) - 5/2*
sqrt(2) + 2)*log(-1/8*(5*(300981*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4) - 1111618*sqrt
(2))*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 - 5558090*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2)
+ 1321) - 5*sqrt(2) - 4)^2 - (1504905*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 + 24078
480*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4) - 213263242*sqrt(2))*(2*sqrt(1/2)*sqrt(941*
sqrt(2) + 1321) + 5*sqrt(2) + 4) - 8*(5*(601962*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 1504905*sqrt(2) - 2315542
)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4) + 11116180*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 27790
450*sqrt(2) - 146566162)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/
2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) + 12) - 3/32*(2
*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 67
3) - 213263242*sqrt(2)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4) - 5544442608*sqrt(2))*sqrt(-sqrt
(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(941*sqrt(2) +
1321) + 5*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(941*s
qrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 673) - 5/2*sqrt(2) + 2)
+ 18101760817*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(4*sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(757
*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1/64*(2
*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) - 18) +
3/4*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 21/8*sqrt(2) - 507/4) - 7*sqrt(2) - 6)*log(1/4*((421182*sqrt(1/2)*sq
rt(757*sqrt(2) - 1063) - 1474137*sqrt(2) + 1389259)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 -
(210591*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 - 10108368*sqrt(1/2)*sqrt(757*sqrt(2) - 1063
) + 35379288*sqrt(2) - 31269425)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6) + 125713*(2*sqrt(1/2)*
sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 8*((210591*sqrt(2)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqr
t(2) + 6) + 125713*sqrt(2))*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6) - 125713*sqrt(2)*(2*sqrt(1/
2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6) + 2072791*sqrt(2))*sqrt(-3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 10
63) + 7*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sq
rt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) - 18) + 3/4*sqrt(1/2
)*sqrt(757*sqrt(2) - 1063) - 21/8*sqrt(2) - 507/4) - 1888642*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 6610247*sqrt
(2) - 86730966)*sqrt(4*sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 - 3/128*(2
*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2
) - 6)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 21/8
*sqrt(2) - 507/4) - 7*sqrt(2) - 6) + 606320225*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - (x^2 - 1)*sqrt(4*sqrt(2)*s
qrt(-3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 10
63) - 7*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(757*sqr
t(2) - 1063) - 7*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 21/8*sqrt(2) - 507/4) - 7*sqrt(2) -
6)*log(-1/4*((421182*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 1474137*sqrt(2) + 1389259)*(2*sqrt(1/2)*sqrt(757*sqr
t(2) - 1063) + 7*sqrt(2) - 6)^2 - (210591*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 - 10108368*
sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 35379288*sqrt(2) - 31269425)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sq
rt(2) - 6) + 125713*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 8*((210591*sqrt(2)*(2*sqrt(1/2)
*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6) + 125713*sqrt(2))*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2)
- 6) - 125713*sqrt(2)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6) + 2072791*sqrt(2))*sqrt(-3/128*(
2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt
(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063)
- 7*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 21/8*sqrt(2) - 507/4) - 1888642*sqrt(1/2)*sqrt(7
57*sqrt(2) - 1063) + 6610247*sqrt(2) - 86730966)*sqrt(4*sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 10
63) + 7*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sq
rt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) - 18) + 3/4*sqrt(1/2
)*sqrt(757*sqrt(2) - 1063) - 21/8*sqrt(2) - 507/4) - 7*sqrt(2) - 6) + 606320225*sqrt(sqrt(x + sqrt(x^2 + 1)) +
1)) + 2*(x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 - 3/128*
(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt
(2) - 6)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 21
/8*sqrt(2) - 507/4) - 7/4*sqrt(2) - 3/2)*log(1/2*((421182*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 1474137*sqrt(2)
+ 1389259)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 - (210591*(2*sqrt(1/2)*sqrt(757*sqrt(2) -
1063) - 7*sqrt(2) + 6)^2 - 10108368*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 35379288*sqrt(2) - 31269425)*(2*sqrt
(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6) + 125713*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6
)^2 - 8*((210591*sqrt(2)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6) + 125713*sqrt(2))*(2*sqrt(1/2)
*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6) - 125713*sqrt(2)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2)
+ 6) + 2072791*sqrt(2))*sqrt(-3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1
/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*
(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 21/8*sqrt(2
) - 507/4) - 1888642*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 6610247*sqrt(2) - 86730966)*sqrt(-sqrt(2)*sqrt(-3/12
8*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*s
qrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 10
63) - 7*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 21/8*sqrt(2) - 507/4) - 7/4*sqrt(2) - 3/2) +
606320225*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 2*(x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(757*sqr
t(2) - 1063) + 7*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1/64*(2*sqr
t(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) - 18) + 3/4
*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 21/8*sqrt(2) - 507/4) - 7/4*sqrt(2) - 3/2)*log(-1/2*((421182*sqrt(1/2)*s
qrt(757*sqrt(2) - 1063) - 1474137*sqrt(2) + 1389259)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2
- (210591*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 - 10108368*sqrt(1/2)*sqrt(757*sqrt(2) - 106
3) + 35379288*sqrt(2) - 31269425)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6) + 125713*(2*sqrt(1/2)
*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 - 8*((210591*sqrt(2)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sq
rt(2) + 6) + 125713*sqrt(2))*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6) - 125713*sqrt(2)*(2*sqrt(1
/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6) + 2072791*sqrt(2))*sqrt(-3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1
063) + 7*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*s
qrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) - 18) + 3/4*sqrt(1/
2)*sqrt(757*sqrt(2) - 1063) - 21/8*sqrt(2) - 507/4) - 1888642*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 6610247*sqr
t(2) - 86730966)*sqrt(-sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 - 3/128*(2
*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2
) - 6)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 21/8
*sqrt(2) - 507/4) - 7/4*sqrt(2) - 3/2) + 606320225*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - (x^2 - 1)*sqrt(2*sqrt(
1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)*log(1/4*(5*(601962*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 1504905
*sqrt(2) - 2315542)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 + 1504905*(2*sqrt(1/2)*sqrt(941*s
qrt(2) + 1321) - 5*sqrt(2) - 4)^3 - (1504905*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 + 481569
60*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 120392400*sqrt(2) - 309577162)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) +
5*sqrt(2) + 4) + 24078480*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 15915875280*sqrt(1/2)*sq
rt(941*sqrt(2) + 1321) + 39789688200*sqrt(2) + 63000481368)*sqrt(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt
(2) + 4) + 18101760817*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321
) + 5*sqrt(2) + 4)*log(-1/4*(5*(601962*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 1504905*sqrt(2) - 2315542)*(2*sqrt
(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4)^2 + 1504905*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2)
- 4)^3 - (1504905*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 + 48156960*sqrt(1/2)*sqrt(941*sqrt(
2) + 1321) - 120392400*sqrt(2) - 309577162)*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4) + 24078480*
(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 15915875280*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 39
789688200*sqrt(2) + 63000481368)*sqrt(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5*sqrt(2) + 4) + 18101760817*sqrt
(sqrt(x + sqrt(x^2 + 1)) + 1)) + 16*(x^2 - 1)*sqrt(-1/128*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5/256*sqrt(2) +
1/64)*log(4*(1504905*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^3 + 29636570*(2*sqrt(1/2)*sqrt(94
1*sqrt(2) + 1321) - 5*sqrt(2) - 4)^2 - 15489348796*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 38723371990*sqrt(2) +
48665202704)*sqrt(-1/128*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5/256*sqrt(2) + 1/64) + 18101760817*sqrt(sqrt(x
+ sqrt(x^2 + 1)) + 1)) - 16*(x^2 - 1)*sqrt(-1/128*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5/256*sqrt(2) + 1/64)*l
og(-4*(1504905*(2*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) - 5*sqrt(2) - 4)^3 + 29636570*(2*sqrt(1/2)*sqrt(941*sqrt(
2) + 1321) - 5*sqrt(2) - 4)^2 - 15489348796*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 38723371990*sqrt(2) + 4866520
2704)*sqrt(-1/128*sqrt(1/2)*sqrt(941*sqrt(2) + 1321) + 5/256*sqrt(2) + 1/64) + 18101760817*sqrt(sqrt(x + sqrt(
x^2 + 1)) + 1)) - (x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*log(1/2*((421182*sqrt(1
/2)*sqrt(757*sqrt(2) - 1063) - 1474137*sqrt(2) + 1389259)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) -
6)^2 + 210591*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^3 - (210591*(2*sqrt(1/2)*sqrt(757*sqrt(2)
- 1063) - 7*sqrt(2) + 6)^2 - 10108368*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 35379288*sqrt(2) - 31269425)*(2*sq
rt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6) - 5054184*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2)
+ 6)^2 + 1799289504*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 6297513264*sqrt(2) + 5950573476)*sqrt(2*sqrt(1/2)*sqr
t(757*sqrt(2) - 1063) + 7*sqrt(2) - 6) + 606320225*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(2*sqrt(
1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)*log(-1/2*((421182*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 1474137*
sqrt(2) + 1389259)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)^2 + 210591*(2*sqrt(1/2)*sqrt(757*sqr
t(2) - 1063) - 7*sqrt(2) + 6)^3 - (210591*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 - 10108368*
sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 35379288*sqrt(2) - 31269425)*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sq
rt(2) - 6) - 5054184*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1799289504*sqrt(1/2)*sqrt(757*
sqrt(2) - 1063) - 6297513264*sqrt(2) + 5950573476)*sqrt(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7*sqrt(2) - 6)
+ 606320225*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 16*(x^2 - 1)*sqrt(-1/128*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) +
7/256*sqrt(2) - 3/128)*log(8*(210591*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^3 - 5179897*(2*sq
rt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1801178146*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 63041235
11*sqrt(2) + 12273741042)*sqrt(-1/128*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7/256*sqrt(2) - 3/128) + 606320225*
sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 16*(x^2 - 1)*sqrt(-1/128*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7/256*sqrt(
2) - 3/128)*log(-8*(210591*(2*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^3 - 5179897*(2*sqrt(1/2)*sqr
t(757*sqrt(2) - 1063) - 7*sqrt(2) + 6)^2 + 1801178146*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) - 6304123511*sqrt(2)
+ 12273741042)*sqrt(-1/128*sqrt(1/2)*sqrt(757*sqrt(2) - 1063) + 7/256*sqrt(2) - 3/128) + 606320225*sqrt(sqrt(x
+ sqrt(x^2 + 1)) + 1)) - 16*sqrt(x + sqrt(x^2 + 1))*x*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1))/(x^2 - 1)
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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.
[In]
integrate((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm="giac")
[Out]
Timed out
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maple [F] time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\left (x^{2}+1\right ) \sqrt {x +\sqrt {x^{2}+1}}\, \sqrt {1+\sqrt {x +\sqrt {x^{2}+1}}}}{\left (-x^{2}+1\right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)
[Out]
int((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{2} + 1\right )} \sqrt {x + \sqrt {x^{2} + 1}} \sqrt {\sqrt {x + \sqrt {x^{2} + 1}} + 1}}{{\left (x^{2} - 1\right )}^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x^2+1)*(x+(x^2+1)^(1/2))^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm="maxima")
[Out]
integrate((x^2 + 1)*sqrt(x + sqrt(x^2 + 1))*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)/(x^2 - 1)^2, x)
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {\sqrt {\sqrt {x+\sqrt {x^2+1}}+1}\,\left (x^2+1\right )\,\sqrt {x+\sqrt {x^2+1}}}{{\left (x^2-1\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((x + (x^2 + 1)^(1/2))^(1/2) + 1)^(1/2)*(x^2 + 1)*(x + (x^2 + 1)^(1/2))^(1/2))/(x^2 - 1)^2,x)
[Out]
int((((x + (x^2 + 1)^(1/2))^(1/2) + 1)^(1/2)*(x^2 + 1)*(x + (x^2 + 1)^(1/2))^(1/2))/(x^2 - 1)^2, x)
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {x + \sqrt {x^{2} + 1}} \left (x^{2} + 1\right ) \sqrt {\sqrt {x + \sqrt {x^{2} + 1}} + 1}}{\left (x - 1\right )^{2} \left (x + 1\right )^{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((x**2+1)*(x+(x**2+1)**(1/2))**(1/2)*(1+(x+(x**2+1)**(1/2))**(1/2))**(1/2)/(-x**2+1)**2,x)
[Out]
Integral(sqrt(x + sqrt(x**2 + 1))*(x**2 + 1)*sqrt(sqrt(x + sqrt(x**2 + 1)) + 1)/((x - 1)**2*(x + 1)**2), x)
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