3.31.6 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx\)
Optimal. Leaf size=404 \[ -\frac {1}{16} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+4 \text {$\#$1}^4-2\& ,\frac {4 \text {$\#$1}^6 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-8 \text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )+\text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )+\log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^7-3 \text {$\#$1}^5+2 \text {$\#$1}^3}\& \right ]+\frac {1}{16} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+8 \text {$\#$1}^4-8 \text {$\#$1}^2+2\& ,\frac {4 \text {$\#$1}^6 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-8 \text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )+7 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-\log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^7-3 \text {$\#$1}^5+4 \text {$\#$1}^3-2 \text {$\#$1}}\& \right ]-\frac {\sqrt {\sqrt {\sqrt {x^2+1}+x}+1} x}{2 \left (x^2-1\right ) \sqrt {\sqrt {x^2+1}+x}} \]
________________________________________________________________________________________
Rubi [F] time = 2.17, 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 {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2 \sqrt {x+\sqrt {1+x^2}}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]
[Out]
Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + Defer[Int][Sqrt[1 + S
qrt[x + Sqrt[1 + x^2]]]/((1 - x)*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]
/((1 + x)^2*Sqrt[x + Sqrt[1 + x^2]]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[x + Sq
rt[1 + x^2]]), x]/4
Rubi steps
\begin {align*} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2 \sqrt {x+\sqrt {1+x^2}}} \, dx &=\int \left (\frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{4 (1-x)^2 \sqrt {x+\sqrt {1+x^2}}}+\frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{4 (1+x)^2 \sqrt {x+\sqrt {1+x^2}}}+\frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 \left (1-x^2\right ) \sqrt {x+\sqrt {1+x^2}}}\right ) \, dx\\ &=\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx+\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx+\frac {1}{2} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right ) \sqrt {x+\sqrt {1+x^2}}} \, dx\\ &=\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx+\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx+\frac {1}{2} \int \left (\frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 (1-x) \sqrt {x+\sqrt {1+x^2}}}+\frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 (1+x) \sqrt {x+\sqrt {1+x^2}}}\right ) \, dx\\ &=\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx+\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x) \sqrt {x+\sqrt {1+x^2}}} \, dx+\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2 \sqrt {x+\sqrt {1+x^2}}} \, dx+\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x) \sqrt {x+\sqrt {1+x^2}}} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [F] time = 9.47, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2 \sqrt {x+\sqrt {1+x^2}}} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]
[Out]
Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]), x]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.67, size = 558, normalized size = 1.38 \begin {gather*} -\frac {x \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 \left (-1+x^2\right ) \sqrt {x+\sqrt {1+x^2}}}-\frac {1}{4} \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {-\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{2 \text {$\#$1}-3 \text {$\#$1}^3+\text {$\#$1}^5}\&\right ]-\frac {1}{16} \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )+5 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2}{2 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]+\frac {1}{4} \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {3 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}-2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^3+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^5}{-2+4 \text {$\#$1}^2-3 \text {$\#$1}^4+\text {$\#$1}^6}\&\right ]-\frac {1}{16} \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )+5 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2}{-2 \text {$\#$1}+4 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ] \end {gather*}
Antiderivative was successfully verified.
[In]
IntegrateAlgebraic[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[x + Sqrt[1 + x^2]]),x]
[Out]
-1/2*(x*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((-1 + x^2)*Sqrt[x + Sqrt[1 + x^2]]) - RootSum[-2 + 4*#1^4 - 4*#1^6
+ #1^8 & , (-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) & ]/4 - RootSum[-2 + 4*#1^4 - 4*#1
^6 + #1^8 & , (Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] + 5*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^
2)/(2*#1^3 - 3*#1^5 + #1^7) & ]/16 + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (3*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) & ]/4 - RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log
[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] + 5*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2)/(-2*#1 + 4*#1^3
- 3*#1^5 + #1^7) & ]/16
________________________________________________________________________________________
fricas [B] time = 2.38, size = 6878, normalized size = 17.02
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm="fricas")
[Out]
-1/32*(sqrt(2)*(x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)^2 - 3
/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 3
9*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) - 24) + 4*sqrt(1/2)*sqrt(1345*sqrt(2) - 223)
- 78*sqrt(2) + 649) - 39/2*sqrt(2) - 4)*log(1/4*((8674646*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*
sqrt(2) + 8) + 295619989*sqrt(2))*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)^2 + 295619989*sqrt(2
)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 - (8674646*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2)
- 223) - 39*sqrt(2) + 8)^2 - 277588672*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8) + 34946
05993*sqrt(2))*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) + 8*((17349292*sqrt(1/2)*sqrt(1345*sqrt
(2) - 223) - 338311194*sqrt(2) + 365017157)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) - 59123997
8*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 11529179571*sqrt(2) + 10589485729)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1345*sq
rt(2) - 223) + 39*sqrt(2) - 8)^2 - 3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16*(2*sq
rt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) - 24) +
4*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 78*sqrt(2) + 649) + 3494605993*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) -
223) - 39*sqrt(2) + 8) - 4975202382104*sqrt(2))*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223)
+ 39*sqrt(2) - 8)^2 - 3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16*(2*sqrt(1/2)*sqrt
(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) - 24) + 4*sqrt(1/2)*
sqrt(1345*sqrt(2) - 223) - 78*sqrt(2) + 649) - 39/2*sqrt(2) - 4) + 14527409494457*sqrt(sqrt(x + sqrt(x^2 + 1))
+ 1)) - sqrt(2)*(x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)^2 -
3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) +
39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) - 24) + 4*sqrt(1/2)*sqrt(1345*sqrt(2) - 22
3) - 78*sqrt(2) + 649) - 39/2*sqrt(2) - 4)*log(-1/4*((8674646*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) -
39*sqrt(2) + 8) + 295619989*sqrt(2))*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)^2 + 295619989*sqr
t(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 - (8674646*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(
2) - 223) - 39*sqrt(2) + 8)^2 - 277588672*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8) + 34
94605993*sqrt(2))*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) + 8*((17349292*sqrt(1/2)*sqrt(1345*s
qrt(2) - 223) - 338311194*sqrt(2) + 365017157)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) - 59123
9978*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 11529179571*sqrt(2) + 10589485729)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1345
*sqrt(2) - 223) + 39*sqrt(2) - 8)^2 - 3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16*(2
*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) - 24)
+ 4*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 78*sqrt(2) + 649) + 3494605993*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2
) - 223) - 39*sqrt(2) + 8) - 4975202382104*sqrt(2))*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 2
23) + 39*sqrt(2) - 8)^2 - 3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16*(2*sqrt(1/2)*s
qrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) - 24) + 4*sqrt(1/
2)*sqrt(1345*sqrt(2) - 223) - 78*sqrt(2) + 649) - 39/2*sqrt(2) - 4) + 14527409494457*sqrt(sqrt(x + sqrt(x^2 +
1)) + 1)) + sqrt(2)*(x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)
^2 - 3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 22
3) + 39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) - 24) + 4*sqrt(1/2)*sqrt(1345*sqrt(2)
- 223) - 78*sqrt(2) + 649) - 39/2*sqrt(2) - 4)*log(1/4*((8674646*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223)
- 39*sqrt(2) + 8) + 295619989*sqrt(2))*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)^2 + 295619989*
sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 - (8674646*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sq
rt(2) - 223) - 39*sqrt(2) + 8)^2 - 277588672*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8) +
3494605993*sqrt(2))*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) - 8*((17349292*sqrt(1/2)*sqrt(134
5*sqrt(2) - 223) - 338311194*sqrt(2) + 365017157)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) - 59
1239978*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 11529179571*sqrt(2) + 10589485729)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1
345*sqrt(2) - 223) + 39*sqrt(2) - 8)^2 - 3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16
*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) -
24) + 4*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 78*sqrt(2) + 649) + 3494605993*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqr
t(2) - 223) - 39*sqrt(2) + 8) - 4975202382104*sqrt(2))*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2)
- 223) + 39*sqrt(2) - 8)^2 - 3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16*(2*sqrt(1/
2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) - 24) + 4*sqr
t(1/2)*sqrt(1345*sqrt(2) - 223) - 78*sqrt(2) + 649) - 39/2*sqrt(2) - 4) + 14527409494457*sqrt(sqrt(x + sqrt(x^
2 + 1)) + 1)) - sqrt(2)*(x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2)
- 8)^2 - 3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16*(2*sqrt(1/2)*sqrt(1345*sqrt(2)
- 223) + 39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) - 24) + 4*sqrt(1/2)*sqrt(1345*sqrt
(2) - 223) - 78*sqrt(2) + 649) - 39/2*sqrt(2) - 4)*log(-1/4*((8674646*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) -
223) - 39*sqrt(2) + 8) + 295619989*sqrt(2))*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)^2 + 29561
9989*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 - (8674646*sqrt(2)*(2*sqrt(1/2)*sqrt(13
45*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 - 277588672*sqrt(2)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) +
8) + 3494605993*sqrt(2))*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) - 8*((17349292*sqrt(1/2)*sqr
t(1345*sqrt(2) - 223) - 338311194*sqrt(2) + 365017157)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)
- 591239978*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 11529179571*sqrt(2) + 10589485729)*sqrt(-3/32*(2*sqrt(1/2)*s
qrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)^2 - 3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 +
1/16*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(
2) - 24) + 4*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 78*sqrt(2) + 649) + 3494605993*sqrt(2)*(2*sqrt(1/2)*sqrt(134
5*sqrt(2) - 223) - 39*sqrt(2) + 8) - 4975202382104*sqrt(2))*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(1345*sq
rt(2) - 223) + 39*sqrt(2) - 8)^2 - 3/32*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 + 1/16*(2*sq
rt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) - 24) +
4*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 78*sqrt(2) + 649) - 39/2*sqrt(2) - 4) + 14527409494457*sqrt(sqrt(x + sq
rt(x^2 + 1)) + 1)) - (x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)*log(1/2*((17349292*
sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 338311194*sqrt(2) + 365017157)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39
*sqrt(2) - 8)^2 + 8674646*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^3 - (8674646*(2*sqrt(1/2)*sq
rt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 - 555177344*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 10825958208*sqrt(2
) + 1273896617)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) - 277588672*(2*sqrt(1/2)*sqrt(1345*sqr
t(2) - 223) - 39*sqrt(2) + 8)^2 - 83415395936*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 1626600220752*sqrt(2) + 525
327569940)*sqrt(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) + 14527409494457*sqrt(sqrt(x + sqrt(x^2
+ 1)) + 1)) + (x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8)*log(-1/2*((17349292*sqrt(
1/2)*sqrt(1345*sqrt(2) - 223) - 338311194*sqrt(2) + 365017157)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt
(2) - 8)^2 + 8674646*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^3 - (8674646*(2*sqrt(1/2)*sqrt(13
45*sqrt(2) - 223) - 39*sqrt(2) + 8)^2 - 555177344*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 10825958208*sqrt(2) + 1
273896617)*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) - 277588672*(2*sqrt(1/2)*sqrt(1345*sqrt(2)
- 223) - 39*sqrt(2) + 8)^2 - 83415395936*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 1626600220752*sqrt(2) + 52532756
9940)*sqrt(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39*sqrt(2) - 8) + 14527409494457*sqrt(sqrt(x + sqrt(x^2 + 1)
) + 1)) + 32*(x^2 - 1)*sqrt(-1/512*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39/1024*sqrt(2) - 1/128)*log(16*(86746
46*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^3 - 573208661*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223)
- 39*sqrt(2) + 8)^2 - 90404607922*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 1762889854479*sqrt(2) + 6762703827012)
*sqrt(-1/512*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39/1024*sqrt(2) - 1/128) + 14527409494457*sqrt(sqrt(x + sqrt
(x^2 + 1)) + 1)) - 32*(x^2 - 1)*sqrt(-1/512*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39/1024*sqrt(2) - 1/128)*log(
-16*(8674646*(2*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) - 39*sqrt(2) + 8)^3 - 573208661*(2*sqrt(1/2)*sqrt(1345*sqrt
(2) - 223) - 39*sqrt(2) + 8)^2 - 90404607922*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 1762889854479*sqrt(2) + 6762
703827012)*sqrt(-1/512*sqrt(1/2)*sqrt(1345*sqrt(2) - 223) + 39/1024*sqrt(2) - 1/128) + 14527409494457*sqrt(sqr
t(x + sqrt(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)*log(1/4*(9
*(1937306*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 39714773*sqrt(2) + 63061452)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 1
61) + 41*sqrt(2) + 10)^2 + 8717877*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^3 - (8717877*(2*sq
rt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 + 697430160*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 1429731
8280*sqrt(2) + 35153973706)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10) + 348715080*(2*sqrt(1/2)*
sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 - 118005183072*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 241910625297
6*sqrt(2) - 1341872612008)*sqrt(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10) + 8529857499113*sqrt(s
qrt(x + sqrt(x^2 + 1)) + 1)) - (x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)*log(-1/4
*(9*(1937306*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 39714773*sqrt(2) + 63061452)*(2*sqrt(1/2)*sqrt(1249*sqrt(2)
+ 161) + 41*sqrt(2) + 10)^2 + 8717877*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^3 - (8717877*(2
*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 + 697430160*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 1429
7318280*sqrt(2) + 35153973706)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10) + 348715080*(2*sqrt(1/
2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 - 118005183072*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 241910625
2976*sqrt(2) - 1341872612008)*sqrt(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10) + 8529857499113*sqr
t(sqrt(x + sqrt(x^2 + 1)) + 1)) - 32*(x^2 - 1)*sqrt(-1/512*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41/1024*sqrt(2
) + 5/512)*log(8*(8717877*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^3 - 306016758*(2*sqrt(1/2)*
sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 - 195287432084*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 400339235772
2*sqrt(2) + 8801481053756)*sqrt(-1/512*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41/1024*sqrt(2) + 5/512) + 8529857
499113*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 32*(x^2 - 1)*sqrt(-1/512*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41/1
024*sqrt(2) + 5/512)*log(-8*(8717877*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^3 - 306016758*(2
*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 - 195287432084*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 4
003392357722*sqrt(2) + 8801481053756)*sqrt(-1/512*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41/1024*sqrt(2) + 5/512
) + 8529857499113*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 2*(x^2 - 1)*sqrt(-41/4*sqrt(2) + 8*sqrt(-3/4096*(2*sqrt
(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2
) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161
) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128) + 5/2)*log(1/4*
(9*(1937306*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 39714773*sqrt(2) + 63061452)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) +
161) + 41*sqrt(2) + 10)^2 - (8717877*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 + 697430160*s
qrt(1/2)*sqrt(1249*sqrt(2) + 161) - 14297318280*sqrt(2) + 35153973706)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) +
41*sqrt(2) + 10) + 654731838*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 + 64*(9*(1937306*sqrt
(1/2)*sqrt(1249*sqrt(2) + 161) - 39714773*sqrt(2) + 63061452)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(
2) + 10) - 1309463676*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 26844005358*sqrt(2) + 18999169366)*sqrt(-3/4096*(2*
sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sq
rt(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2) +
161) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128) + 772822490
12*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 1584286104746*sqrt(2) - 4886990310052)*sqrt(-41/4*sqrt(2) + 8*sqrt(-3/
4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161)
+ 41*sqrt(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(1249*s
qrt(2) + 161) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128) + 5
/2) + 8529857499113*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 2*(x^2 - 1)*sqrt(-41/4*sqrt(2) + 8*sqrt(-3/4096*(2*sq
rt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt
(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 1
61) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128) + 5/2)*log(-1
/4*(9*(1937306*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 39714773*sqrt(2) + 63061452)*(2*sqrt(1/2)*sqrt(1249*sqrt(2
) + 161) + 41*sqrt(2) + 10)^2 - (8717877*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 + 69743016
0*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 14297318280*sqrt(2) + 35153973706)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161
) + 41*sqrt(2) + 10) + 654731838*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 + 64*(9*(1937306*s
qrt(1/2)*sqrt(1249*sqrt(2) + 161) - 39714773*sqrt(2) + 63061452)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sq
rt(2) + 10) - 1309463676*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 26844005358*sqrt(2) + 18999169366)*sqrt(-3/4096*
(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41
*sqrt(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2
) + 161) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128) + 772822
49012*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 1584286104746*sqrt(2) - 4886990310052)*sqrt(-41/4*sqrt(2) + 8*sqrt(
-3/4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 1
61) + 41*sqrt(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(124
9*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128)
+ 5/2) + 8529857499113*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 2*(x^2 - 1)*sqrt(-41/4*sqrt(2) - 8*sqrt(-3/4096*(2
*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*s
qrt(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2)
+ 161) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128) + 5/2)*log
(1/4*(9*(1937306*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 39714773*sqrt(2) + 63061452)*(2*sqrt(1/2)*sqrt(1249*sqrt
(2) + 161) + 41*sqrt(2) + 10)^2 - (8717877*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 + 697430
160*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 14297318280*sqrt(2) + 35153973706)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 1
61) + 41*sqrt(2) + 10) + 654731838*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 - 64*(9*(1937306
*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 39714773*sqrt(2) + 63061452)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*
sqrt(2) + 10) - 1309463676*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 26844005358*sqrt(2) + 18999169366)*sqrt(-3/409
6*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) +
41*sqrt(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(1249*sqrt
(2) + 161) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128) + 7728
2249012*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 1584286104746*sqrt(2) - 4886990310052)*sqrt(-41/4*sqrt(2) - 8*sqr
t(-3/4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) +
161) + 41*sqrt(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(1
249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128
) + 5/2) + 8529857499113*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 2*(x^2 - 1)*sqrt(-41/4*sqrt(2) - 8*sqrt(-3/4096*
(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41
*sqrt(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2
) + 161) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128) + 5/2)*l
og(-1/4*(9*(1937306*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 39714773*sqrt(2) + 63061452)*(2*sqrt(1/2)*sqrt(1249*s
qrt(2) + 161) + 41*sqrt(2) + 10)^2 - (8717877*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 + 697
430160*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 14297318280*sqrt(2) + 35153973706)*(2*sqrt(1/2)*sqrt(1249*sqrt(2)
+ 161) + 41*sqrt(2) + 10) + 654731838*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 - 64*(9*(1937
306*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 39714773*sqrt(2) + 63061452)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) +
41*sqrt(2) + 10) - 1309463676*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 26844005358*sqrt(2) + 18999169366)*sqrt(-3/
4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161)
+ 41*sqrt(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqrt(1249*s
qrt(2) + 161) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/128) + 7
7282249012*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 1584286104746*sqrt(2) - 4886990310052)*sqrt(-41/4*sqrt(2) - 8*
sqrt(-3/4096*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 41*sqrt(2) + 10)^2 + 1/2048*(2*sqrt(1/2)*sqrt(1249*sqrt(2
) + 161) + 41*sqrt(2) + 10)*(2*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) - 41*sqrt(2) + 30) - 3/4096*(2*sqrt(1/2)*sqr
t(1249*sqrt(2) + 161) - 41*sqrt(2) - 10)^2 - 5/128*sqrt(1/2)*sqrt(1249*sqrt(2) + 161) + 205/256*sqrt(2) + 921/
128) + 5/2) + 8529857499113*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 16*(x^2 - sqrt(x^2 + 1)*x)*sqrt(x + sqrt(x^2
+ 1))*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1))/(x^2 - 1)
________________________________________________________________________________________
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((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm="giac")
[Out]
Timed out
________________________________________________________________________________________
maple [F] time = 0.05, size = 0, normalized size = 0.00 \[\int \frac {\sqrt {1+\sqrt {x +\sqrt {x^{2}+1}}}}{\left (-x^{2}+1\right )^{2} \sqrt {x +\sqrt {x^{2}+1}}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)
[Out]
int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x)
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {\sqrt {x + \sqrt {x^{2} + 1}} + 1}}{{\left (x^{2} - 1\right )}^{2} \sqrt {x + \sqrt {x^{2} + 1}}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x+(x^2+1)^(1/2))^(1/2),x, algorithm="maxima")
[Out]
integrate(sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)/((x^2 - 1)^2*sqrt(x + sqrt(x^2 + 1))), x)
________________________________________________________________________________________
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 )}^2\,\sqrt {x+\sqrt {x^2+1}}} \,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)^2*(x + (x^2 + 1)^(1/2))^(1/2)),x)
[Out]
int(((x + (x^2 + 1)^(1/2))^(1/2) + 1)^(1/2)/((x^2 - 1)^2*(x + (x^2 + 1)^(1/2))^(1/2)), x)
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {\sqrt {x + \sqrt {x^{2} + 1}} + 1}}{\left (x - 1\right )^{2} \left (x + 1\right )^{2} \sqrt {x + \sqrt {x^{2} + 1}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((1+(x+(x**2+1)**(1/2))**(1/2))**(1/2)/(-x**2+1)**2/(x+(x**2+1)**(1/2))**(1/2),x)
[Out]
Integral(sqrt(sqrt(x + sqrt(x**2 + 1)) + 1)/((x - 1)**2*(x + 1)**2*sqrt(x + sqrt(x**2 + 1))), x)
________________________________________________________________________________________