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

Optimal. Leaf size=357 \[ \frac {1}{16} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+8 \text {$\#$1}^4-8 \text {$\#$1}^2+2\& ,\frac {3 \text {$\#$1}^3 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-2 \text {$\#$1} \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^6-3 \text {$\#$1}^4+4 \text {$\#$1}^2-2}\& \right ]-\frac {1}{16} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+4 \text {$\#$1}^4-2\& ,\frac {3 \text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-2 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^7-3 \text {$\#$1}^5+2 \text {$\#$1}^3}\& \right ]+\frac {\left (-3 x^2-1\right ) \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-3 x \sqrt {x^2+1} \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}}{2 \left (2 x^2+1\right ) \left (x^2-1\right )+4 x \sqrt {x^2+1} \left (x^2-1\right )} \]

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Rubi [F]  time = 1.64, 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+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[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]

[Out]

Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[
1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1
+ x)^2, x]/4 + Defer[Int][(Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4

Rubi steps

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

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Mathematica [A]  time = 0.23, size = 365, normalized size = 1.02 \begin {gather*} \frac {\left (x^2+\sqrt {x^2+1} x+1\right ) \left (\text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+8 \text {$\#$1}^4-8 \text {$\#$1}^2+2\&,\frac {3 \text {$\#$1}^3 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-2 \text {$\#$1} \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^6-3 \text {$\#$1}^4+4 \text {$\#$1}^2-2}\&\right ]-\text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+4 \text {$\#$1}^4-2\&,\frac {3 \text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-2 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^7-3 \text {$\#$1}^5+2 \text {$\#$1}^3}\&\right ]-\frac {8 \sqrt {\sqrt {\sqrt {x^2+1}+x}+1} \left (3 x^2+3 \sqrt {x^2+1} x+1\right )}{\left (x^2-1\right ) \left (2 x^2+2 \sqrt {x^2+1} x+1\right )}\right )}{16 \sqrt {x^2+1} \left (\sqrt {x^2+1}+x\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

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IntegrateAlgebraic [A]  time = 0.00, size = 537, normalized size = 1.50 \begin {gather*} \frac {\left (-1-3 x^2\right ) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-3 x \sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{4 x \left (-1+x^2\right ) \sqrt {1+x^2}+2 \left (-1+x^2\right ) \left (1+2 x^2\right )}+\text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )}{2 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]-\frac {1}{16} \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {14 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+3 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{2 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]+\text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )}{-2 \text {$\#$1}+4 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]+\frac {1}{16} \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {-16 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+3 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{-2 \text {$\#$1}+4 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ] \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((-1 - 3*x^2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 3*x*Sqrt[1 + x^2]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(4*x*(-
1 + x^2)*Sqrt[1 + x^2] + 2*(-1 + x^2)*(1 + 2*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 - 3*#1^5 + #1^7) & ] - RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (14*Log[Sqrt
[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 3*Log[Sqrt[1 + Sqrt
[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(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]/(-2*#1 + 4*#1^3 - 3*#1^5 + #1^7) & ] + RootSum[2 - 8*#1^2 + 8
*#1^4 - 4*#1^6 + #1^8 & , (-16*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 +
x^2]]] - #1]*#1^2 + 3*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(-2*#1 + 4*#1^3 - 3*#1^5 + #1^7) & ]/1
6

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fricas [B]  time = 2.05, size = 6606, normalized size = 18.50

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm="fricas")

[Out]

-1/16*(sqrt(1/2)*(x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)*log(1/4*sqrt(1/2)*(10203*(2*
sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^3 + (20406*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 10203*sqrt(2) - 1
48696)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 + 571368*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt
(2) - 14)^2 - 3*(3401*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 380912*sqrt(1/2)*sqrt(85*sqrt(2)
- 41) + 190456*sqrt(2) - 2723784)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) + 27262416*sqrt(1/2)*sqrt
(85*sqrt(2) - 41) + 13631208*sqrt(2) - 192953624)*sqrt(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) + 825
917*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - sqrt(1/2)*(x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2)
+ 14)*log(-1/4*sqrt(1/2)*(10203*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^3 + (20406*sqrt(1/2)*sqrt(8
5*sqrt(2) - 41) + 10203*sqrt(2) - 148696)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 + 571368*(2*sqr
t(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 - 3*(3401*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2
+ 380912*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 190456*sqrt(2) - 2723784)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt
(2) + 14) + 27262416*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 13631208*sqrt(2) - 192953624)*sqrt(2*sqrt(1/2)*sqrt(85*
sqrt(2) - 41) - sqrt(2) + 14) + 825917*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - sqrt(1/2)*(x^2 - 1)*sqrt(2*sqrt(1/
2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)*log(1/4*sqrt(1/2)*((6150*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 3075*sqrt(
2) - 129614)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 + 3075*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) -
sqrt(2) - 16)^3 - 3*(1025*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 + 131200*sqrt(1/2)*sqrt(65*sqrt
(2) + 47) - 65600*sqrt(2) - 1943144)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16) + 196800*(2*sqrt(1/2)*
sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 + 8265600*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 4132800*sqrt(2) - 75955768
)*sqrt(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16) + 10121717*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + sqrt(
1/2)*(x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)*log(-1/4*sqrt(1/2)*((6150*sqrt(1/2)*sqrt
(65*sqrt(2) + 47) - 3075*sqrt(2) - 129614)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 + 3075*(2*sqrt
(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^3 - 3*(1025*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 +
131200*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 65600*sqrt(2) - 1943144)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2
) + 16) + 196800*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 + 8265600*sqrt(1/2)*sqrt(65*sqrt(2) + 47
) - 4132800*sqrt(2) - 75955768)*sqrt(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16) + 10121717*sqrt(sqrt(x
+ sqrt(x^2 + 1)) + 1)) - (x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^
2 + 1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) + 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)
- 3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 7/2*sqrt(2)
- 20) + 1/2*sqrt(2) + 7)*log(1/8*((20406*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 10203*sqrt(2) - 148696)*(2*sqrt(1/
2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 5854*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 - 3*(34
01*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 380912*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 190456*sqrt
(2) - 2723784)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) + 4*sqrt(-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2)
- 41) + sqrt(2) - 14)^2 + 1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) + 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2)
- 41) - sqrt(2) + 14) - 3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(
2) - 41) - 7/2*sqrt(2) - 20)*((10203*sqrt(2)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14) - 5854*sqrt(2)
)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) + 5854*sqrt(2)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(
2) - 14) + 155624*sqrt(2)) - 344400*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 172200*sqrt(2) - 282720)*sqrt(sqrt(2)*sq
rt(-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt
(2) + 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) - 3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(
2) + 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 7/2*sqrt(2) - 20) + 1/2*sqrt(2) + 7) + 825917*sqrt(sqrt(x + s
qrt(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 +
1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) + 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) -
3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 7/2*sqrt(2) -
20) + 1/2*sqrt(2) + 7)*log(-1/8*((20406*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 10203*sqrt(2) - 148696)*(2*sqrt(1/2)
*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 5854*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 - 3*(3401
*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 380912*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 190456*sqrt(2
) - 2723784)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) + 4*sqrt(-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) -
41) + sqrt(2) - 14)^2 + 1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) + 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) -
41) - sqrt(2) + 14) - 3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2)
- 41) - 7/2*sqrt(2) - 20)*((10203*sqrt(2)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14) - 5854*sqrt(2))*
(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) + 5854*sqrt(2)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2)
- 14) + 155624*sqrt(2)) - 344400*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 172200*sqrt(2) - 282720)*sqrt(sqrt(2)*sqrt
(-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2
) + 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) - 3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2)
+ 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 7/2*sqrt(2) - 20) + 1/2*sqrt(2) + 7) + 825917*sqrt(sqrt(x + sqr
t(x^2 + 1)) + 1)) - (x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 +
1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) + 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) - 3
/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 7/2*sqrt(2) - 2
0) + 1/2*sqrt(2) + 7)*log(1/8*((20406*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 10203*sqrt(2) - 148696)*(2*sqrt(1/2)*s
qrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 5854*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 - 3*(3401*(
2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 380912*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 190456*sqrt(2)
- 2723784)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) - 4*sqrt(-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41
) + sqrt(2) - 14)^2 + 1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) + 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 4
1) - sqrt(2) + 14) - 3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2) -
41) - 7/2*sqrt(2) - 20)*((10203*sqrt(2)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14) - 5854*sqrt(2))*(2
*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) + 5854*sqrt(2)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) -
14) + 155624*sqrt(2)) - 344400*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 172200*sqrt(2) - 282720)*sqrt(-sqrt(2)*sqrt(
-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2)
+ 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) - 3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2)
+ 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 7/2*sqrt(2) - 20) + 1/2*sqrt(2) + 7) + 825917*sqrt(sqrt(x + sqrt
(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 1
/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) + 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) - 3/
32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 7/2*sqrt(2) - 20
) + 1/2*sqrt(2) + 7)*log(-1/8*((20406*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 10203*sqrt(2) - 148696)*(2*sqrt(1/2)*s
qrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 5854*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 - 3*(3401*(
2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 380912*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 190456*sqrt(2)
- 2723784)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) - 4*sqrt(-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41
) + sqrt(2) - 14)^2 + 1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) + 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 4
1) - sqrt(2) + 14) - 3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2) -
41) - 7/2*sqrt(2) - 20)*((10203*sqrt(2)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14) - 5854*sqrt(2))*(2
*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) + 5854*sqrt(2)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) -
14) + 155624*sqrt(2)) - 344400*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 172200*sqrt(2) - 282720)*sqrt(-sqrt(2)*sqrt(
-3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 1/16*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2)
+ 42)*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2) + 14) - 3/32*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - sqrt(2)
+ 14)^2 - 7*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 7/2*sqrt(2) - 20) + 1/2*sqrt(2) + 7) + 825917*sqrt(sqrt(x + sqrt
(x^2 + 1)) + 1)) - 16*(x^2 - 1)*sqrt(-1/256*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 1/512*sqrt(2) + 7/256)*log(4*(10
203*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^3 + 577222*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2)
- 14)^2 + 27606816*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + 13803408*sqrt(2) - 47309512)*sqrt(-1/256*sqrt(1/2)*sqrt(
85*sqrt(2) - 41) - 1/512*sqrt(2) + 7/256) + 825917*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 16*(x^2 - 1)*sqrt(-1/2
56*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 1/512*sqrt(2) + 7/256)*log(-4*(10203*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) +
sqrt(2) - 14)^3 + 577222*(2*sqrt(1/2)*sqrt(85*sqrt(2) - 41) + sqrt(2) - 14)^2 + 27606816*sqrt(1/2)*sqrt(85*sq
rt(2) - 41) + 13803408*sqrt(2) - 47309512)*sqrt(-1/256*sqrt(1/2)*sqrt(85*sqrt(2) - 41) - 1/512*sqrt(2) + 7/256
) + 825917*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 16*(x^2 - 1)*sqrt(-1/256*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/5
12*sqrt(2) + 1/32)*log(4*(3075*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^3 + 277214*(2*sqrt(1/2)*sqrt
(65*sqrt(2) + 47) - sqrt(2) - 16)^2 + 13626864*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 6813432*sqrt(2) - 64497944)*s
qrt(-1/256*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/512*sqrt(2) + 1/32) + 10121717*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1
)) - 16*(x^2 - 1)*sqrt(-1/256*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/512*sqrt(2) + 1/32)*log(-4*(3075*(2*sqrt(1/2
)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^3 + 277214*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 + 1362
6864*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 6813432*sqrt(2) - 64497944)*sqrt(-1/256*sqrt(1/2)*sqrt(65*sqrt(2) + 47)
+ 1/512*sqrt(2) + 1/32) + 10121717*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 2*(x^2 - 1)*sqrt(-1/8*sqrt(2) + sqrt(
-3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 + 1/128*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(
2) + 16)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) + 48) - 3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(
2) - 16)^2 - sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/2*sqrt(2) + 3) + 2)*log(1/4*((6150*sqrt(1/2)*sqrt(65*sqrt(2)
+ 47) - 3075*sqrt(2) - 129614)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 - 3*(1025*(2*sqrt(1/2)*sqr
t(65*sqrt(2) + 47) - sqrt(2) - 16)^2 + 131200*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 65600*sqrt(2) - 1943144)*(2*sq
rt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16) - 80414*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 + 1
6*((6150*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 3075*sqrt(2) - 129614)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2)
+ 16) + 160828*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 80414*sqrt(2) + 1179240)*sqrt(-3/256*(2*sqrt(1/2)*sqrt(65*sq
rt(2) + 47) + sqrt(2) + 16)^2 + 1/128*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)*(2*sqrt(1/2)*sqrt(65*
sqrt(2) + 47) - sqrt(2) + 48) - 3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 - sqrt(1/2)*sqrt(65
*sqrt(2) + 47) + 1/2*sqrt(2) + 3) - 5361264*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 2680632*sqrt(2) + 4214512)*sqrt(
-1/8*sqrt(2) + sqrt(-3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 + 1/128*(2*sqrt(1/2)*sqrt(65*s
qrt(2) + 47) + sqrt(2) + 16)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) + 48) - 3/256*(2*sqrt(1/2)*sqrt(65*s
qrt(2) + 47) - sqrt(2) - 16)^2 - sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/2*sqrt(2) + 3) + 2) + 10121717*sqrt(sqrt(
x + sqrt(x^2 + 1)) + 1)) - 2*(x^2 - 1)*sqrt(-1/8*sqrt(2) + sqrt(-3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sq
rt(2) + 16)^2 + 1/128*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) -
sqrt(2) + 48) - 3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 - sqrt(1/2)*sqrt(65*sqrt(2) + 47) +
1/2*sqrt(2) + 3) + 2)*log(-1/4*((6150*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 3075*sqrt(2) - 129614)*(2*sqrt(1/2)*s
qrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 - 3*(1025*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 + 131200
*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 65600*sqrt(2) - 1943144)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)
- 80414*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 + 16*((6150*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 30
75*sqrt(2) - 129614)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16) + 160828*sqrt(1/2)*sqrt(65*sqrt(2) + 4
7) - 80414*sqrt(2) + 1179240)*sqrt(-3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 + 1/128*(2*sqrt
(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) + 48) - 3/256*(2*sqrt
(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 - sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/2*sqrt(2) + 3) - 5361264*s
qrt(1/2)*sqrt(65*sqrt(2) + 47) + 2680632*sqrt(2) + 4214512)*sqrt(-1/8*sqrt(2) + sqrt(-3/256*(2*sqrt(1/2)*sqrt(
65*sqrt(2) + 47) + sqrt(2) + 16)^2 + 1/128*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)*(2*sqrt(1/2)*sqr
t(65*sqrt(2) + 47) - sqrt(2) + 48) - 3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 - sqrt(1/2)*sq
rt(65*sqrt(2) + 47) + 1/2*sqrt(2) + 3) + 2) + 10121717*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 2*(x^2 - 1)*sqrt(-
1/8*sqrt(2) - sqrt(-3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 + 1/128*(2*sqrt(1/2)*sqrt(65*sq
rt(2) + 47) + sqrt(2) + 16)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) + 48) - 3/256*(2*sqrt(1/2)*sqrt(65*sq
rt(2) + 47) - sqrt(2) - 16)^2 - sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/2*sqrt(2) + 3) + 2)*log(1/4*((6150*sqrt(1/
2)*sqrt(65*sqrt(2) + 47) - 3075*sqrt(2) - 129614)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 - 3*(10
25*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 + 131200*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 65600*sqrt(
2) - 1943144)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16) - 80414*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) -
sqrt(2) - 16)^2 - 16*((6150*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 3075*sqrt(2) - 129614)*(2*sqrt(1/2)*sqrt(65*sqrt
(2) + 47) + sqrt(2) + 16) + 160828*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 80414*sqrt(2) + 1179240)*sqrt(-3/256*(2*s
qrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 + 1/128*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)*(2
*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) + 48) - 3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2
- sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/2*sqrt(2) + 3) - 5361264*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 2680632*sqrt(
2) + 4214512)*sqrt(-1/8*sqrt(2) - sqrt(-3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 + 1/128*(2*
sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) + 48) - 3/256*(2*
sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 - sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/2*sqrt(2) + 3) + 2) +
10121717*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 2*(x^2 - 1)*sqrt(-1/8*sqrt(2) - sqrt(-3/256*(2*sqrt(1/2)*sqrt(65
*sqrt(2) + 47) + sqrt(2) + 16)^2 + 1/128*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)*(2*sqrt(1/2)*sqrt(
65*sqrt(2) + 47) - sqrt(2) + 48) - 3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 - sqrt(1/2)*sqrt
(65*sqrt(2) + 47) + 1/2*sqrt(2) + 3) + 2)*log(-1/4*((6150*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 3075*sqrt(2) - 129
614)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 - 3*(1025*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(
2) - 16)^2 + 131200*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - 65600*sqrt(2) - 1943144)*(2*sqrt(1/2)*sqrt(65*sqrt(2) +
47) + sqrt(2) + 16) - 80414*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 - 16*((6150*sqrt(1/2)*sqrt(65
*sqrt(2) + 47) - 3075*sqrt(2) - 129614)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16) + 160828*sqrt(1/2)*
sqrt(65*sqrt(2) + 47) - 80414*sqrt(2) + 1179240)*sqrt(-3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16
)^2 + 1/128*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) +
48) - 3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 16)^2 - sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/2*sqrt(
2) + 3) - 5361264*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 2680632*sqrt(2) + 4214512)*sqrt(-1/8*sqrt(2) - sqrt(-3/256
*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 16)^2 + 1/128*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) + sqrt(2) + 1
6)*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) + 48) - 3/256*(2*sqrt(1/2)*sqrt(65*sqrt(2) + 47) - sqrt(2) - 1
6)^2 - sqrt(1/2)*sqrt(65*sqrt(2) + 47) + 1/2*sqrt(2) + 3) + 2) + 10121717*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) -
8*(x^2 - sqrt(x^2 + 1)*x - 1)*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)^(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 \[\int \frac {\sqrt {x^{2}+1}\, \sqrt {1+\sqrt {x +\sqrt {x^{2}+1}}}}{\left (-x^{2}+1\right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^2+1)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)

[Out]

int((x^2+1)^(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^{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)^(1/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm="maxima")

[Out]

integrate(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^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)^(1/2))/(x^2 - 1)^2,x)

[Out]

int((((x + (x^2 + 1)^(1/2))^(1/2) + 1)^(1/2)*(x^2 + 1)^(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^{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**2+1)**(1/2)*(1+(x+(x**2+1)**(1/2))**(1/2))**(1/2)/(-x**2+1)**2,x)

[Out]

Integral(sqrt(x**2 + 1)*sqrt(sqrt(x + sqrt(x**2 + 1)) + 1)/((x - 1)**2*(x + 1)**2), x)

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