3.31.2 \(\int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)

Optimal. Leaf size=401 \[ -\frac {1}{16} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+4 \text {$\#$1}^4-2\& ,\frac {\text {$\#$1}^6 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-\text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )+3 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )+\log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^7-3 \text {$\#$1}^5+2 \text {$\#$1}^3}\& \right ]-\frac {1}{16} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+8 \text {$\#$1}^4-8 \text {$\#$1}^2+2\& ,\frac {\text {$\#$1}^6 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-\text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-5 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )+\log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^7-3 \text {$\#$1}^5+4 \text {$\#$1}^3-2 \text {$\#$1}}\& \right ]-\frac {\sqrt {\sqrt {x^2+1}+x} \sqrt {\sqrt {\sqrt {x^2+1}+x}+1} x}{2 \left (x^2-1\right )} \]

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Rubi [F]  time = 1.69, 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 {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[(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]/4 + Defer[Int][(Sqrt[x +
Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 +
Sqrt[x + Sqrt[1 + x^2]]])/(1 + x)^2, x]/4 + Defer[Int][(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^
2]]])/(1 + x), x]/4

Rubi steps

\begin {align*} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2} \, dx &=\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\\ &=\frac {1}{4} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2} \, dx+\frac {1}{4} \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}{4} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2} \, dx+\frac {1}{4} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2} \, dx+\frac {1}{2} \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}{4} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2} \, dx+\frac {1}{4} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x} \, dx+\frac {1}{4} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2} \, dx+\frac {1}{4} \int \frac {\sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1+x} \, dx\\ \end {align*}

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Mathematica [F]  time = 0.38, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\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[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]

[Out]

Integrate[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2, x]

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IntegrateAlgebraic [A]  time = 0.00, size = 552, normalized size = 1.38 \begin {gather*} -\frac {x \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 \left (-1+x^2\right )}+\frac {1}{4} \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )}{2 \text {$\#$1}-3 \text {$\#$1}^3+\text {$\#$1}^5}\&\right ]-\frac {1}{16} \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )+7 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2-\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^6}{2 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]-\frac {1}{4} \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}}{-2+4 \text {$\#$1}^2-3 \text {$\#$1}^4+\text {$\#$1}^6}\&\right ]-\frac {1}{16} \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-9 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2-\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^6}{-2 \text {$\#$1}+4 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ] \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[(Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]

[Out]

-1/2*(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 & , Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]/(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] + 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) & ]/16 - 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 + 4*#1^2 - 3*#1^4 + #1^6) & ]/4 - RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (Log[Sq
rt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 9*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 + 4*#1^3 - 3*#1^5 +
#1^7) & ]/16

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fricas [B]  time = 2.05, size = 6966, normalized size = 17.37

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((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]

-1/32*(sqrt(2)*(x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 1/
16*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) +
12) - 3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37
*sqrt(2) + 913) - 37/2*sqrt(2) + 2)*log(1/8*((7252423*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2
) - 4) - 86307886*sqrt(2))*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 - 86307886*sqrt(2)*(2*sqrt
(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - (7252423*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37
*sqrt(2) - 4)^2 + 116038768*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4) - 10516321158*sqrt(
2))*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4) + 8*((14504846*sqrt(1/2)*sqrt(877*sqrt(2) + 457) -
268339651*sqrt(2) - 115317578)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4) + 172615772*sqrt(1/2)*sq
rt(877*sqrt(2) + 457) - 3193391782*sqrt(2) - 9480626526)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*
sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 4
57) - 37*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(877*
sqrt(2) + 457) + 37*sqrt(2) + 913) - 10516321158*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4
) - 128487844240*sqrt(2))*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 1
/16*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) +
12) - 3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 3
7*sqrt(2) + 913) - 37/2*sqrt(2) + 2) + 1238984819345*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - sqrt(2)*(x^2 - 1)*sq
rt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(877*sq
rt(2) + 457) + 37*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqr
t(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 913) - 37/2*sqrt
(2) + 2)*log(-1/8*((7252423*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4) - 86307886*sqrt(2))
*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 - 86307886*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 4
57) - 37*sqrt(2) - 4)^2 - (7252423*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 + 11603876
8*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4) - 10516321158*sqrt(2))*(2*sqrt(1/2)*sqrt(877*
sqrt(2) + 457) + 37*sqrt(2) + 4) + 8*((14504846*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 268339651*sqrt(2) - 115317
578)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4) + 172615772*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 31
93391782*sqrt(2) - 9480626526)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 1/16*(2*s
qrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) + 12) - 3
/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2
) + 913) - 10516321158*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4) - 128487844240*sqrt(2))*
sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(877*
sqrt(2) + 457) + 37*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*s
qrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 913) - 37/2*sq
rt(2) + 2) + 1238984819345*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + sqrt(2)*(x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/32*(2*
sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2)
+ 4)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37
*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 913) - 37/2*sqrt(2) + 2)*log(1/8*((725242
3*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4) - 86307886*sqrt(2))*(2*sqrt(1/2)*sqrt(877*sqr
t(2) + 457) + 37*sqrt(2) + 4)^2 - 86307886*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 -
(7252423*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 + 116038768*sqrt(2)*(2*sqrt(1/2)*sqr
t(877*sqrt(2) + 457) - 37*sqrt(2) - 4) - 10516321158*sqrt(2))*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2
) + 4) - 8*((14504846*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 268339651*sqrt(2) - 115317578)*(2*sqrt(1/2)*sqrt(877
*sqrt(2) + 457) + 37*sqrt(2) + 4) + 172615772*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 3193391782*sqrt(2) - 9480626
526)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(877*sqrt(2)
+ 457) + 37*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(877*
sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 913) - 10516321158*sqr
t(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4) - 128487844240*sqrt(2))*sqrt(-sqrt(2)*sqrt(-3/32*(
2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(
2) + 4)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) -
37*sqrt(2) - 4)^2 - 2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 913) - 37/2*sqrt(2) + 2) + 123898481934
5*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - sqrt(2)*(x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2
) + 457) + 37*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)*(2*sqrt(1/2)*sqrt(8
77*sqrt(2) + 457) - 37*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 2*sqrt(
1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 913) - 37/2*sqrt(2) + 2)*log(-1/8*((7252423*sqrt(2)*(2*sqrt(1/2)*s
qrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4) - 86307886*sqrt(2))*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2)
+ 4)^2 - 86307886*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - (7252423*sqrt(2)*(2*sqrt
(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 + 116038768*sqrt(2)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 3
7*sqrt(2) - 4) - 10516321158*sqrt(2))*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4) - 8*((14504846*sq
rt(1/2)*sqrt(877*sqrt(2) + 457) - 268339651*sqrt(2) - 115317578)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqr
t(2) + 4) + 172615772*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 3193391782*sqrt(2) - 9480626526)*sqrt(-3/32*(2*sqrt(
1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)
*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt
(2) - 4)^2 - 2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 913) - 10516321158*sqrt(2)*(2*sqrt(1/2)*sqrt(8
77*sqrt(2) + 457) - 37*sqrt(2) - 4) - 128487844240*sqrt(2))*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(877*sqr
t(2) + 457) + 37*sqrt(2) + 4)^2 + 1/16*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)*(2*sqrt(1/2)*sqr
t(877*sqrt(2) + 457) - 37*sqrt(2) + 12) - 3/32*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 2*sq
rt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 913) - 37/2*sqrt(2) + 2) + 1238984819345*sqrt(sqrt(x + sqrt(x^2
+ 1)) + 1)) - (x^2 - 1)*sqrt(4*sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 -
3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) +
39*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(725*sqrt(2) - 263
) - 117/8*sqrt(2) + 629/4) - 39*sqrt(2) - 6)*log(1/4*((10631262*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 207309609*
sqrt(2) - 45701129)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 - (5315631*(2*sqrt(1/2)*sqrt(725*
sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 255150288*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 4975430616*sqrt(2) - 159218
44073)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6) - 77594915*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263)
- 39*sqrt(2) + 6)^2 + 8*((5315631*sqrt(2)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6) - 77594915*sq
rt(2))*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6) + 77594915*sqrt(2)*(2*sqrt(1/2)*sqrt(725*sqrt(2)
- 263) - 39*sqrt(2) + 6) - 17018671169*sqrt(2))*sqrt(-3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2)
- 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(725*sqrt(2)
- 263) + 39*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(725*sqrt
(2) - 263) - 117/8*sqrt(2) + 629/4) - 30312786418*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 591099335151*sqrt(2) - 8
50010185254)*sqrt(4*sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 - 3/128*(2*sq
rt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) -
6)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 117/8*sq
rt(2) + 629/4) - 39*sqrt(2) - 6) + 4949244239297*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(4*sqrt(2)
*sqrt(-3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) -
263) - 39*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(725*s
qrt(2) - 263) - 39*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 117/8*sqrt(2) + 629/4) - 39*sqrt(2)
- 6)*log(-1/4*((10631262*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 207309609*sqrt(2) - 45701129)*(2*sqrt(1/2)*sqrt(
725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 - (5315631*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 2
55150288*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 4975430616*sqrt(2) - 15921844073)*(2*sqrt(1/2)*sqrt(725*sqrt(2) -
263) + 39*sqrt(2) - 6) - 77594915*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 + 8*((5315631*sqrt
(2)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6) - 77594915*sqrt(2))*(2*sqrt(1/2)*sqrt(725*sqrt(2) -
263) + 39*sqrt(2) - 6) + 77594915*sqrt(2)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6) - 1701867116
9*sqrt(2))*sqrt(-3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(725*
sqrt(2) - 263) - 39*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)*(2*sqrt(1/2)*
sqrt(725*sqrt(2) - 263) - 39*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 117/8*sqrt(2) + 629/4) -
30312786418*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 591099335151*sqrt(2) - 850010185254)*sqrt(4*sqrt(2)*sqrt(-3/12
8*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*s
qrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 26
3) - 39*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 117/8*sqrt(2) + 629/4) - 39*sqrt(2) - 6) + 494
9244239297*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 2*(x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(725*sq
rt(2) - 263) + 39*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 + 1/64*(2*sq
rt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) - 18) + 3/
4*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 117/8*sqrt(2) + 629/4) - 39/4*sqrt(2) - 3/2)*log(1/2*((10631262*sqrt(1/2
)*sqrt(725*sqrt(2) - 263) - 207309609*sqrt(2) - 45701129)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) -
6)^2 - (5315631*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 255150288*sqrt(1/2)*sqrt(725*sqrt(2
) - 263) + 4975430616*sqrt(2) - 15921844073)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6) - 77594915
*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 8*((5315631*sqrt(2)*(2*sqrt(1/2)*sqrt(725*sqrt(2)
- 263) - 39*sqrt(2) + 6) - 77594915*sqrt(2))*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6) + 77594915
*sqrt(2)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6) - 17018671169*sqrt(2))*sqrt(-3/128*(2*sqrt(1/2
)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2
+ 1/64*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(
2) - 18) + 3/4*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 117/8*sqrt(2) + 629/4) - 30312786418*sqrt(1/2)*sqrt(725*sqr
t(2) - 263) + 591099335151*sqrt(2) - 850010185254)*sqrt(-sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 2
63) + 39*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*s
qrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) - 18) + 3/4*sqrt(1/
2)*sqrt(725*sqrt(2) - 263) - 117/8*sqrt(2) + 629/4) - 39/4*sqrt(2) - 3/2) + 4949244239297*sqrt(sqrt(x + sqrt(x
^2 + 1)) + 1)) + 2*(x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^
2 - 3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263)
+ 39*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(725*sqrt(2) -
263) - 117/8*sqrt(2) + 629/4) - 39/4*sqrt(2) - 3/2)*log(-1/2*((10631262*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 20
7309609*sqrt(2) - 45701129)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 - (5315631*(2*sqrt(1/2)*s
qrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 255150288*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 4975430616*sqrt(2)
- 15921844073)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6) - 77594915*(2*sqrt(1/2)*sqrt(725*sqrt(2)
- 263) - 39*sqrt(2) + 6)^2 - 8*((5315631*sqrt(2)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6) - 775
94915*sqrt(2))*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6) + 77594915*sqrt(2)*(2*sqrt(1/2)*sqrt(725
*sqrt(2) - 263) - 39*sqrt(2) + 6) - 17018671169*sqrt(2))*sqrt(-3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39
*sqrt(2) - 6)^2 - 3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(725*
sqrt(2) - 263) + 39*sqrt(2) - 6)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(
725*sqrt(2) - 263) - 117/8*sqrt(2) + 629/4) - 30312786418*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 591099335151*sqr
t(2) - 850010185254)*sqrt(-sqrt(2)*sqrt(-3/128*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 - 3/12
8*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 + 1/64*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sq
rt(2) - 6)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) - 18) + 3/4*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 1
17/8*sqrt(2) + 629/4) - 39/4*sqrt(2) - 3/2) + 4949244239297*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - (x^2 - 1)*sqr
t(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)*log(1/4*((14504846*sqrt(1/2)*sqrt(877*sqrt(2) + 457) -
268339651*sqrt(2) - 115317578)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 7252423*(2*sqrt(1/2
)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^3 - (7252423*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4
)^2 + 232077536*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 4293434416*sqrt(2) - 10980476230)*(2*sqrt(1/2)*sqrt(877*sq
rt(2) + 457) + 37*sqrt(2) + 4) + 116038768*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 10455092
9968*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 1934192204408*sqrt(2) + 822369864488)*sqrt(2*sqrt(1/2)*sqrt(877*sqrt(
2) + 457) + 37*sqrt(2) + 4) + 1238984819345*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(2*sqrt(1/2)*sq
rt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)*log(-1/4*((14504846*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 268339651*sqrt
(2) - 115317578)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*sqrt(2) + 4)^2 + 7252423*(2*sqrt(1/2)*sqrt(877*sqrt
(2) + 457) - 37*sqrt(2) - 4)^3 - (7252423*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 + 232077536
*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 4293434416*sqrt(2) - 10980476230)*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) +
37*sqrt(2) + 4) + 116038768*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 104550929968*sqrt(1/2)*
sqrt(877*sqrt(2) + 457) + 1934192204408*sqrt(2) + 822369864488)*sqrt(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37*
sqrt(2) + 4) + 1238984819345*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 32*(x^2 - 1)*sqrt(-1/512*sqrt(1/2)*sqrt(877*
sqrt(2) + 457) + 37/1024*sqrt(2) + 1/256)*log(8*(7252423*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4
)^3 + 202346654*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 83518287652*sqrt(1/2)*sqrt(877*sqrt
(2) + 457) + 1545088321562*sqrt(2) + 2897193593136)*sqrt(-1/512*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37/1024*sq
rt(2) + 1/256) + 1238984819345*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 32*(x^2 - 1)*sqrt(-1/512*sqrt(1/2)*sqrt(87
7*sqrt(2) + 457) + 37/1024*sqrt(2) + 1/256)*log(-8*(7252423*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2)
- 4)^3 + 202346654*(2*sqrt(1/2)*sqrt(877*sqrt(2) + 457) - 37*sqrt(2) - 4)^2 - 83518287652*sqrt(1/2)*sqrt(877*s
qrt(2) + 457) + 1545088321562*sqrt(2) + 2897193593136)*sqrt(-1/512*sqrt(1/2)*sqrt(877*sqrt(2) + 457) + 37/1024
*sqrt(2) + 1/256) + 1238984819345*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(725*sqr
t(2) - 263) + 39*sqrt(2) - 6)*log(1/2*((10631262*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 207309609*sqrt(2) - 45701
129)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 + 5315631*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) -
39*sqrt(2) + 6)^3 - (5315631*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 255150288*sqrt(1/2)*s
qrt(725*sqrt(2) - 263) + 4975430616*sqrt(2) - 15921844073)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) -
6) - 127575144*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 51200157792*sqrt(1/2)*sqrt(725*sqrt
(2) - 263) + 998403076944*sqrt(2) + 803856604292)*sqrt(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6) +
4949244239297*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - (x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sq
rt(2) - 6)*log(-1/2*((10631262*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 207309609*sqrt(2) - 45701129)*(2*sqrt(1/2)*
sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6)^2 + 5315631*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^3
- (5315631*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 255150288*sqrt(1/2)*sqrt(725*sqrt(2) -
263) + 4975430616*sqrt(2) - 15921844073)*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6) - 127575144*(2
*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 51200157792*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 99840
3076944*sqrt(2) + 803856604292)*sqrt(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39*sqrt(2) - 6) + 4949244239297*sqr
t(sqrt(x + sqrt(x^2 + 1)) + 1)) - 32*(x^2 - 1)*sqrt(-1/512*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39/1024*sqrt(2)
- 3/512)*log(16*(5315631*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^3 - 49980229*(2*sqrt(1/2)*sqr
t(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 20887371374*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 407303741793*sqrt(2
) + 1701058629730)*sqrt(-1/512*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39/1024*sqrt(2) - 3/512) + 4949244239297*sq
rt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 32*(x^2 - 1)*sqrt(-1/512*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39/1024*sqrt(2
) - 3/512)*log(-16*(5315631*(2*sqrt(1/2)*sqrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^3 - 49980229*(2*sqrt(1/2)*s
qrt(725*sqrt(2) - 263) - 39*sqrt(2) + 6)^2 - 20887371374*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 407303741793*sqrt
(2) + 1701058629730)*sqrt(-1/512*sqrt(1/2)*sqrt(725*sqrt(2) - 263) + 39/1024*sqrt(2) - 3/512) + 4949244239297*
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+(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 = 0.00, size = 0, normalized size = 0.00 \[\int \frac {\sqrt {x +\sqrt {x^{2}+1}}\, \sqrt {1+\sqrt {x +\sqrt {x^{2}+1}}}}{\left (-x^{2}+1\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x+(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+(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 {\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+(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(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}\,\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 + (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 + (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}} \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+(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))*sqrt(sqrt(x + sqrt(x**2 + 1)) + 1)/((x - 1)**2*(x + 1)**2), x)

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