3.30.54 \(\int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2 \sqrt {1+x^2}} \, dx\)
Optimal. Leaf size=357 \[ \frac {1}{32} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+8 \text {$\#$1}^4-8 \text {$\#$1}^2+2\& ,\frac {11 \text {$\#$1}^3 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-10 \text {$\#$1} \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^6-3 \text {$\#$1}^4+4 \text {$\#$1}^2-2}\& \right ]-\frac {1}{32} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+4 \text {$\#$1}^4-2\& ,\frac {11 \text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-10 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^7-3 \text {$\#$1}^5+2 \text {$\#$1}^3}\& \right ]+\frac {\left (-3 x^2-1\right ) \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-3 x \sqrt {x^2+1} \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}}{4 \left (2 x^2+1\right ) \left (x^2-1\right )+8 x \sqrt {x^2+1} \left (x^2-1\right )} \]
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Rubi [F] time = 2.26, 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 {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[1 + x^2]),x]
[Out]
Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x)^2*Sqrt[1 + x^2]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sq
rt[1 + x^2]]]/((1 - x)*Sqrt[1 + x^2]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)^2*Sqrt[1 +
x^2]), x]/4 + Defer[Int][Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 + x)*Sqrt[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 {1+x^2}} \, dx &=\int \left (\frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{4 (1-x)^2 \sqrt {1+x^2}}+\frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{4 (1+x)^2 \sqrt {1+x^2}}+\frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 \left (1-x^2\right ) \sqrt {1+x^2}}\right ) \, dx\\ &=\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2 \sqrt {1+x^2}} \, dx+\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2 \sqrt {1+x^2}} \, dx+\frac {1}{2} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right ) \sqrt {1+x^2}} \, dx\\ &=\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2 \sqrt {1+x^2}} \, dx+\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2 \sqrt {1+x^2}} \, dx+\frac {1}{2} \int \left (\frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 (1-x) \sqrt {1+x^2}}+\frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 (1+x) \sqrt {1+x^2}}\right ) \, dx\\ &=\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2 \sqrt {1+x^2}} \, dx+\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x) \sqrt {1+x^2}} \, dx+\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2 \sqrt {1+x^2}} \, dx+\frac {1}{4} \int \frac {\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x) \sqrt {1+x^2}} \, dx\\ \end {align*}
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Mathematica [A] time = 0.69, size = 365, normalized size = 1.02 \begin {gather*} \frac {\left (x^2+\sqrt {x^2+1} x+1\right ) \left (\text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+8 \text {$\#$1}^4-8 \text {$\#$1}^2+2\&,\frac {11 \text {$\#$1}^3 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-10 \text {$\#$1} \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^6-3 \text {$\#$1}^4+4 \text {$\#$1}^2-2}\&\right ]-\text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+4 \text {$\#$1}^4-2\&,\frac {11 \text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-10 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^7-3 \text {$\#$1}^5+2 \text {$\#$1}^3}\&\right ]-\frac {8 \sqrt {\sqrt {\sqrt {x^2+1}+x}+1} \left (3 x^2+3 \sqrt {x^2+1} x+1\right )}{\left (x^2-1\right ) \left (2 x^2+2 \sqrt {x^2+1} x+1\right )}\right )}{32 \sqrt {x^2+1} \left (\sqrt {x^2+1}+x\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[1 + x^2]),x]
[Out]
((1 + x^2 + x*Sqrt[1 + x^2])*((-8*(1 + 3*x^2 + 3*x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/((-1 + x^
2)*(1 + 2*x^2 + 2*x*Sqrt[1 + x^2])) - RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (-2*Log[Sqrt[1 + Sqrt[x + Sqrt[1
+ x^2]]] - #1] - 10*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + 11*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]
]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] + RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-10*Log[Sqrt[1
+ Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1 + 11*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1
^4 + #1^6) & ]))/(32*Sqrt[1 + x^2]*(x + Sqrt[1 + x^2]))
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IntegrateAlgebraic [A] time = 0.61, size = 640, normalized size = 1.79 \begin {gather*} \frac {\left (-1-3 x^2\right ) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-3 x \sqrt {1+x^2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{8 x \left (-1+x^2\right ) \sqrt {1+x^2}+4 \left (-1+x^2\right ) \left (1+2 x^2\right )}-\frac {1}{4} \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2}{-\text {$\#$1}^3+\text {$\#$1}^5}\&\right ]-\frac {1}{32} \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {14 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+3 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{2 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]+\frac {1}{4} \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{-2 \text {$\#$1}+4 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]+\frac {1}{32} \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {-16 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+3 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{-2 \text {$\#$1}+4 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ] \end {gather*}
Antiderivative was successfully verified.
[In]
IntegrateAlgebraic[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]/((1 - x^2)^2*Sqrt[1 + x^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]]])/(8*x*(-
1 + x^2)*Sqrt[1 + x^2] + 4*(-1 + x^2)*(1 + 2*x^2)) - RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (Log[Sqrt[1 + Sqr
t[x + Sqrt[1 + x^2]]] - #1] + Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2)/(-#1^3 + #1^5) & ]/4 - 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 + Sqr
t[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) & ]/32
+ RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 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 + 4*#1^3 - 3*
#1^5 + #1^7) & ]/4 + 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) & ]/32
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fricas [B] time = 2.38, size = 6616, normalized size = 18.53
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^2+1)^(1/2),x, algorithm="fricas")
[Out]
-1/32*(sqrt(1/2)*(x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142)*log(1/4*sqrt(1/2)*(6074
5595*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^3 + 5*(24298238*sqrt(1/2)*sqrt(7829*sqrt(2) + 447
1) + 12149119*sqrt(2) - 20528023336)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142)^2 + 34503497960*(
2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 - (60745595*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) +
sqrt(2) - 142)^2 + 69006995920*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 34503497960*sqrt(2) - 31673245796728)*(2*
sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) + 12525255724240*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 62
62627862120*sqrt(2) - 2184991273150072)*sqrt(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) + 42912356
58222877*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - sqrt(1/2)*(x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) -
sqrt(2) + 142)*log(-1/4*sqrt(1/2)*(60745595*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^3 + 5*(24
298238*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 12149119*sqrt(2) - 20528023336)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) +
4471) - sqrt(2) + 142)^2 + 34503497960*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 - (60745595*(
2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 69006995920*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 3
4503497960*sqrt(2) - 31673245796728)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) + 12525255724240*
sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 6262627862120*sqrt(2) - 2184991273150072)*sqrt(2*sqrt(1/2)*sqrt(7829*sqr
t(2) + 4471) - sqrt(2) + 142) + 4291235658222877*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - sqrt(1/2)*(x^2 - 1)*sqrt
(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*log(1/4*sqrt(1/2)*((117039366*sqrt(1/2)*sqrt(7585*sqrt
(2) - 4273) - 58519683*sqrt(2) - 98569616782)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)^2 + 5851
9683*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^3 - (58519683*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 42
73) - sqrt(2) - 144)^2 + 67414674816*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 33707337408*sqrt(2) - 3078354956904
8)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144) + 33707337408*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273
) - sqrt(2) - 144)^2 + 16561538446464*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 8280769223232*sqrt(2) - 3603682878
484760)*sqrt(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144) + 4075668248272853*sqrt(sqrt(x + sqrt(x^2
+ 1)) + 1)) + sqrt(1/2)*(x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*log(-1/4*sqrt(1/
2)*((117039366*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 58519683*sqrt(2) - 98569616782)*(2*sqrt(1/2)*sqrt(7585*sq
rt(2) - 4273) + sqrt(2) + 144)^2 + 58519683*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^3 - (58519
683*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 + 67414674816*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273
) - 33707337408*sqrt(2) - 30783549569048)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144) + 3370733740
8*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 + 16561538446464*sqrt(1/2)*sqrt(7585*sqrt(2) - 427
3) - 8280769223232*sqrt(2) - 3603682878484760)*sqrt(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144) + 4
075668248272853*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - (x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(7829*
sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) + 426)*(2*sqrt(1/2)
*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142)^2 -
71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*sqrt(2) + 2236) + 1/2*sqrt(2) + 71)*log(1/8*(5*(24298238*sqrt(1
/2)*sqrt(7829*sqrt(2) + 4471) + 12149119*sqrt(2) - 20528023336)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(
2) + 142)^2 - 94014242190*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 - (60745595*(2*sqrt(1/2)*s
qrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 69006995920*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 34503497960*sq
rt(2) - 31673245796728)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) + 4*sqrt(-3/32*(2*sqrt(1/2)*sq
rt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) + 426)*(2*s
qrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) +
142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*sqrt(2) + 2236)*(5*(12149119*sqrt(2)*(2*sqrt(1/2)*sqrt(
7829*sqrt(2) + 4471) + sqrt(2) - 142) - 18802848438*sqrt(2))*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2)
+ 142) + 94014242190*sqrt(2)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142) + 26626340477512*sqrt(2))
- 53547498172816*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 26773749086408*sqrt(2) + 2132045369314336)*sqrt(sqrt(2
)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(7829*sqrt(2) +
4471) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(7829*
sqrt(2) + 4471) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*sqrt(2) + 2236) + 1/2*sqrt(
2) + 71) + 4291235658222877*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2
)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) + 426)*
(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2
) + 142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*sqrt(2) + 2236) + 1/2*sqrt(2) + 71)*log(-1/8*(5*(24
298238*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 12149119*sqrt(2) - 20528023336)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) +
4471) - sqrt(2) + 142)^2 - 94014242190*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 - (60745595*(
2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 69006995920*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 3
4503497960*sqrt(2) - 31673245796728)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) + 4*sqrt(-3/32*(2
*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2
) + 426)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471)
- sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*sqrt(2) + 2236)*(5*(12149119*sqrt(2)*(2*sq
rt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142) - 18802848438*sqrt(2))*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 447
1) - sqrt(2) + 142) + 94014242190*sqrt(2)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142) + 2662634047
7512*sqrt(2)) - 53547498172816*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 26773749086408*sqrt(2) + 2132045369314336
)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(7
829*sqrt(2) + 4471) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3/32*(2*sqrt(1/
2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*sqrt(2) + 2236
) + 1/2*sqrt(2) + 71) + 4291235658222877*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - (x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/
32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + s
qrt(2) + 426)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) +
4471) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*sqrt(2) + 2236) + 1/2*sqrt(2) + 71)*l
og(1/8*(5*(24298238*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 12149119*sqrt(2) - 20528023336)*(2*sqrt(1/2)*sqrt(78
29*sqrt(2) + 4471) - sqrt(2) + 142)^2 - 94014242190*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2
- (60745595*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 69006995920*sqrt(1/2)*sqrt(7829*sqrt(2
) + 4471) + 34503497960*sqrt(2) - 31673245796728)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 4*
sqrt(-3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4
471) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(7829*sq
rt(2) + 4471) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*sqrt(2) + 2236)*(5*(12149119*
sqrt(2)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142) - 18802848438*sqrt(2))*(2*sqrt(1/2)*sqrt(7829*
sqrt(2) + 4471) - sqrt(2) + 142) + 94014242190*sqrt(2)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)
+ 26626340477512*sqrt(2)) - 53547498172816*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 26773749086408*sqrt(2) + 213
2045369314336)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sq
rt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3
/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*
sqrt(2) + 2236) + 1/2*sqrt(2) + 71) + 4291235658222877*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + (x^2 - 1)*sqrt(-sq
rt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(7829*sqrt(
2) + 4471) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(7
829*sqrt(2) + 4471) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*sqrt(2) + 2236) + 1/2*s
qrt(2) + 71)*log(-1/8*(5*(24298238*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 12149119*sqrt(2) - 20528023336)*(2*sq
rt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142)^2 - 94014242190*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sq
rt(2) - 142)^2 - (60745595*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 69006995920*sqrt(1/2)*s
qrt(7829*sqrt(2) + 4471) + 34503497960*sqrt(2) - 31673245796728)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt
(2) + 142) - 4*sqrt(-3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(7
829*sqrt(2) + 4471) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) - 3/32*(2*sqrt(1/
2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 71/2*sqrt(2) + 2236
)*(5*(12149119*sqrt(2)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142) - 18802848438*sqrt(2))*(2*sqrt(
1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142) + 94014242190*sqrt(2)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) +
sqrt(2) - 142) + 26626340477512*sqrt(2)) - 53547498172816*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 2677374908640
8*sqrt(2) + 2132045369314336)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)
^2 + 1/16*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqr
t(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(7829*sqrt(2)
+ 4471) - 71/2*sqrt(2) + 2236) + 1/2*sqrt(2) + 71) + 4291235658222877*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 32*
(x^2 - 1)*sqrt(-1/1024*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 1/2048*sqrt(2) + 71/1024)*log(8*(60745595*(2*sqrt
(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^3 + 128517740150*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqr
t(2) - 142)^2 + 66072753897056*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 33036376948528*sqrt(2) - 3015947399062824
)*sqrt(-1/1024*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 1/2048*sqrt(2) + 71/1024) + 4291235658222877*sqrt(sqrt(x
+ sqrt(x^2 + 1)) + 1)) + 32*(x^2 - 1)*sqrt(-1/1024*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 1/2048*sqrt(2) + 71/1
024)*log(-8*(60745595*(2*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^3 + 128517740150*(2*sqrt(1/2)*sq
rt(7829*sqrt(2) + 4471) + sqrt(2) - 142)^2 + 66072753897056*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) + 330363769485
28*sqrt(2) - 3015947399062824)*sqrt(-1/1024*sqrt(1/2)*sqrt(7829*sqrt(2) + 4471) - 1/2048*sqrt(2) + 71/1024) +
4291235658222877*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 32*(x^2 - 1)*sqrt(-1/1024*sqrt(1/2)*sqrt(7585*sqrt(2) -
4273) + 1/2048*sqrt(2) + 9/128)*log(8*(58519683*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^3 + 12
3850119838*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 + 68420924411056*sqrt(1/2)*sqrt(7585*sqrt
(2) - 4273) - 34210462205528*sqrt(2) - 1521001659221560)*sqrt(-1/1024*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 1/
2048*sqrt(2) + 9/128) + 4075668248272853*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 32*(x^2 - 1)*sqrt(-1/1024*sqrt(1
/2)*sqrt(7585*sqrt(2) - 4273) + 1/2048*sqrt(2) + 9/128)*log(-8*(58519683*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273
) - sqrt(2) - 144)^3 + 123850119838*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 + 68420924411056
*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 34210462205528*sqrt(2) - 1521001659221560)*sqrt(-1/1024*sqrt(1/2)*sqrt(
7585*sqrt(2) - 4273) + 1/2048*sqrt(2) + 9/128) + 4075668248272853*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(7585*sqrt(2) - 4273) + sqrt(2) + 144)^2 + 1/128*(2*sqrt
(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) + 432) - 3/2
56*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 9/2*sqr
t(2) - 267) + 18)*log(1/4*((117039366*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 58519683*sqrt(2) - 98569616782)*(2
*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)^2 - (58519683*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - s
qrt(2) - 144)^2 + 67414674816*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 33707337408*sqrt(2) - 30783549569048)*(2*s
qrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144) - 90142782430*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqr
t(2) - 144)^2 + 16*((117039366*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 58519683*sqrt(2) - 98569616782)*(2*sqrt(1
/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144) + 180285564860*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 9014278243
0*sqrt(2) + 13011989027464)*sqrt(-3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)^2 + 1/128*(2*s
qrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) + 432) -
3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 9/2*
sqrt(2) - 267) - 51859385964592*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 25929692982296*sqrt(2) - 198303993412692
8)*sqrt(-1/8*sqrt(2) + sqrt(-3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1
/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) + 432) - 3/256
*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 9/2*sqrt(
2) - 267) + 18) + 4075668248272853*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(7585*sqrt(2) - 4273) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273)
+ sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(
2) - 4273) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 9/2*sqrt(2) - 267) + 18)*log(-1/4*((11
7039366*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 58519683*sqrt(2) - 98569616782)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) -
4273) + sqrt(2) + 144)^2 - (58519683*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 + 67414674816*
sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 33707337408*sqrt(2) - 30783549569048)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4
273) + sqrt(2) + 144) - 90142782430*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 + 16*((117039366
*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 58519683*sqrt(2) - 98569616782)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273)
+ sqrt(2) + 144) + 180285564860*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 90142782430*sqrt(2) + 13011989027464)*sq
rt(-3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4
273) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(7585*s
qrt(2) - 4273) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 9/2*sqrt(2) - 267) - 5185938596459
2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 25929692982296*sqrt(2) - 1983039934126928)*sqrt(-1/8*sqrt(2) + sqrt(-3
/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273)
+ sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2
) - 4273) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 9/2*sqrt(2) - 267) + 18) + 407566824827
2853*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(7585*s
qrt(2) - 4273) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*(2*sqrt(1/2)
*sqrt(7585*sqrt(2) - 4273) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2
- 9*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 9/2*sqrt(2) - 267) + 18)*log(1/4*((117039366*sqrt(1/2)*sqrt(7585*sqr
t(2) - 4273) - 58519683*sqrt(2) - 98569616782)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)^2 - (58
519683*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 + 67414674816*sqrt(1/2)*sqrt(7585*sqrt(2) - 4
273) - 33707337408*sqrt(2) - 30783549569048)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144) - 9014278
2430*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 - 16*((117039366*sqrt(1/2)*sqrt(7585*sqrt(2) -
4273) - 58519683*sqrt(2) - 98569616782)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144) + 180285564860
*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 90142782430*sqrt(2) + 13011989027464)*sqrt(-3/256*(2*sqrt(1/2)*sqrt(758
5*sqrt(2) - 4273) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*(2*sqrt(1
/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)
^2 - 9*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 9/2*sqrt(2) - 267) - 51859385964592*sqrt(1/2)*sqrt(7585*sqrt(2) -
4273) + 25929692982296*sqrt(2) - 1983039934126928)*sqrt(-1/8*sqrt(2) - sqrt(-3/256*(2*sqrt(1/2)*sqrt(7585*sqr
t(2) - 4273) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*(2*sqrt(1/2)*s
qrt(7585*sqrt(2) - 4273) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 -
9*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 9/2*sqrt(2) - 267) + 18) + 4075668248272853*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(7585*sqrt(2) - 4273) + sqrt(2) + 144)
^2 + 1/128*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sq
rt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(7585*sqrt(2)
- 4273) + 9/2*sqrt(2) - 267) + 18)*log(-1/4*((117039366*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 58519683*sqrt(2
) - 98569616782)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)^2 - (58519683*(2*sqrt(1/2)*sqrt(7585*
sqrt(2) - 4273) - sqrt(2) - 144)^2 + 67414674816*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 33707337408*sqrt(2) - 3
0783549569048)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144) - 90142782430*(2*sqrt(1/2)*sqrt(7585*sq
rt(2) - 4273) - sqrt(2) - 144)^2 - 16*((117039366*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - 58519683*sqrt(2) - 985
69616782)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144) + 180285564860*sqrt(1/2)*sqrt(7585*sqrt(2) -
4273) - 90142782430*sqrt(2) + 13011989027464)*sqrt(-3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) +
144)^2 + 1/128*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273)
- sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(7585*sqr
t(2) - 4273) + 9/2*sqrt(2) - 267) - 51859385964592*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + 25929692982296*sqrt(2
) - 1983039934126928)*sqrt(-1/8*sqrt(2) - sqrt(-3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)^
2 + 1/128*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqr
t(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(7585*sqrt(2) - 4273) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(7585*sqrt(2)
- 4273) + 9/2*sqrt(2) - 267) + 18) + 4075668248272853*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)
________________________________________________________________________________________
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^2+1)^(1/2),x, algorithm="giac")
[Out]
Timed out
________________________________________________________________________________________
maple [F] time = 0.07, size = 0, normalized size = 0.00 \[\int \frac {\sqrt {1+\sqrt {x +\sqrt {x^{2}+1}}}}{\left (-x^{2}+1\right )^{2} \sqrt {x^{2}+1}}\, dx\]
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^2+1)^(1/2),x)
[Out]
int((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x^2+1)^(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}}{\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]
integrate((1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2/(x^2+1)^(1/2),x, algorithm="maxima")
[Out]
integrate(sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)/(sqrt(x^2 + 1)*(x^2 - 1)^2), 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^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^2 + 1)^(1/2)),x)
[Out]
int(((x + (x^2 + 1)^(1/2))^(1/2) + 1)^(1/2)/((x^2 - 1)^2*(x^2 + 1)^(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^{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**2+1)**(1/2),x)
[Out]
Integral(sqrt(sqrt(x + sqrt(x**2 + 1)) + 1)/((x - 1)**2*(x + 1)**2*sqrt(x**2 + 1)), x)
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