∫ (1+x2)5∕2∘ ___________ 1+∘ _______ x+√ ___ 1+x2 _____________________________________________

3.32.7 $\int \frac {(1+x^2)^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx$

Optimal. Leaf size=603 \[ -\frac {1}{4} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+8 \text {$\#$1}^4-8 \text {$\#$1}^2+2\& ,\frac {13 \text {$\#$1}^3 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-14 \text {$\#$1} \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^6-3 \text {$\#$1}^4+4 \text {$\#$1}^2-2}\& \right ]+\frac {1}{4} \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+4 \text {$\#$1}^4-2\& ,\frac {13 \text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-14 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )+2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^7-3 \text {$\#$1}^5+2 \text {$\#$1}^3}\& \right ]-\frac {2299}{128} \tanh ^{-1}\left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}\right )+\frac {\sqrt {\sqrt {x^2+1}+x} \sqrt {\sqrt {\sqrt {x^2+1}+x}+1} \left (10240 x^7+8192 x^6-3740 x^5-1680 x^4-8025 x^3-6328 x^2+1525 x-184\right )+\sqrt {x^2+1} \left (\sqrt {\sqrt {x^2+1}+x} \sqrt {\sqrt {\sqrt {x^2+1}+x}+1} \left (10240 x^6+8192 x^5-8860 x^4-5776 x^3-2315 x^2-2416 x+935\right )+\left (143360 x^7-12288 x^6+5789696 x^5+7272 x^4-3989088 x^3+5298 x^2-3314848 x-282\right ) \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}\right )+\left (143360 x^8-12288 x^7+5861376 x^6+1128 x^5-1112160 x^4+10470 x^3-6024144 x^2+690 x-803792\right ) \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}}{40320 \left (x^2-1\right ) \left (8 x^4+8 x^2+1\right )+40320 \left (x^2-1\right ) \sqrt {x^2+1} \left (8 x^3+4 x\right )} \]

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Rubi [F] time = 1.75, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac {\text {number of rules}}{\text {integrand size}}$ = 0.000, Rules used = {} \begin {gather*} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]

[Out]

Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x)^2, x]/4 + Defer[Int][((1 + x^2)^(5/2)*S

qrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x), x]/4 + Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]

])/(1 + x)^2, x]/4 + Defer[Int][((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 + x), x]/4

Rubi steps

\begin {align*} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{\left (1-x^2\right )^2} \, dx &=\int \left (\frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{4 (1-x)^2}+\frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{4 (1+x)^2}+\frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 \left (1-x^2\right )}\right ) \, dx\\ &=\frac {1}{4} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2} \, dx+\frac {1}{4} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2} \, dx+\frac {1}{2} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x^2} \, dx\\ &=\frac {1}{4} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2} \, dx+\frac {1}{4} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2} \, dx+\frac {1}{2} \int \left (\frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 (1-x)}+\frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{2 (1+x)}\right ) \, dx\\ &=\frac {1}{4} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x)^2} \, dx+\frac {1}{4} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1-x} \, dx+\frac {1}{4} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1+x)^2} \, dx+\frac {1}{4} \int \frac {\left (1+x^2\right )^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{1+x} \, dx\\ \end {align*}

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Mathematica [A] time = 0.59, size = 765, normalized size = 1.27 \begin {gather*} \frac {\left (x^2+1\right )^{3/2} \left (\sqrt {x^2+1}+x\right ) \left (-20160 \left (\sqrt {x^2+1}+x\right )^2 \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+8 \text {$\#$1}^4-8 \text {$\#$1}^2+2\&,\frac {13 \text {$\#$1}^3 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-14 \text {$\#$1} \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^6-3 \text {$\#$1}^4+4 \text {$\#$1}^2-2}\&\right ]+20160 \left (\sqrt {x^2+1}+x\right )^2 \text {RootSum}\left [\text {$\#$1}^8-4 \text {$\#$1}^6+4 \text {$\#$1}^4-2\&,\frac {13 \text {$\#$1}^4 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )-14 \text {$\#$1}^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )+2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\text {$\#$1}\right )}{\text {$\#$1}^7-3 \text {$\#$1}^5+2 \text {$\#$1}^3}\&\right ]+8960 \left (\sqrt {x^2+1}+x\right )^2 \left (\sqrt {\sqrt {x^2+1}+x}+1\right )^{9/2}-34560 \left (\sqrt {x^2+1}+x\right )^2 \left (\sqrt {\sqrt {x^2+1}+x}+1\right )^{7/2}+48384 \left (\sqrt {x^2+1}+x\right )^2 \left (\sqrt {\sqrt {x^2+1}+x}+1\right )^{5/2}-26880 \left (\sqrt {x^2+1}+x\right )^2 \left (\sqrt {\sqrt {x^2+1}+x}+1\right )^{3/2}+1451520 \left (\sqrt {x^2+1}+x\right )^2 \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-3150 \left (\sqrt {x^2+1}+x\right )^{3/2} \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}+2100 \left (\sqrt {x^2+1}+x\right ) \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-\frac {161280 \left (3 x^2+3 \sqrt {x^2+1} x+1\right ) \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}}{x^2-1}-1680 \sqrt {\sqrt {x^2+1}+x} \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}-10080 \sqrt {\sqrt {\sqrt {x^2+1}+x}+1}+724185 \left (\sqrt {x^2+1}+x\right )^2 \log \left (1-\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}\right )-724185 \left (\sqrt {x^2+1}+x\right )^2 \log \left (\sqrt {\sqrt {\sqrt {x^2+1}+x}+1}+1\right )\right )}{80640 \left (x^2+\sqrt {x^2+1} x+1\right )^3} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]

[Out]

((1 + x^2)^(3/2)*(x + Sqrt[1 + x^2])*(-10080*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 1680*Sqrt[x + Sqrt[1 + x^2]]*

Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 2100*(x + Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - 3150*(x + Sqr

t[1 + x^2])^(3/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + 1451520*(x + Sqrt[1 + x^2])^2*Sqrt[1 + Sqrt[x + Sqrt[1 +

x^2]]] - (161280*(1 + 3*x^2 + 3*x*Sqrt[1 + x^2])*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(-1 + x^2) - 26880*(x + S

qrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(3/2) + 48384*(x + Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]]

)^(5/2) - 34560*(x + Sqrt[1 + x^2])^2*(1 + Sqrt[x + Sqrt[1 + x^2]])^(7/2) + 8960*(x + Sqrt[1 + x^2])^2*(1 + Sq

rt[x + Sqrt[1 + x^2]])^(9/2) + 724185*(x + Sqrt[1 + x^2])^2*Log[1 - Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] - 72418

5*(x + Sqrt[1 + x^2])^2*Log[1 + Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]] + 20160*(x + Sqrt[1 + x^2])^2*RootSum[-2 +

4*#1^4 - 4*#1^6 + #1^8 & , (2*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - 14*Log[Sqrt[1 + Sqrt[x + Sqrt[1 +

x^2]]] - #1]*#1^2 + 13*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(2*#1^3 - 3*#1^5 + #1^7) & ] - 20160*

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

]] - #1]*#1 + 13*Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^3)/(-2 + 4*#1^2 - 3*#1^4 + #1^6) & ]))/(80640*

(1 + x^2 + x*Sqrt[1 + x^2])^3)

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IntegrateAlgebraic [A] time = 0.00, size = 921, normalized size = 1.53 \begin {gather*} \frac {\left (-803792+690 x-6024144 x^2+10470 x^3-1112160 x^4+1128 x^5+5861376 x^6-12288 x^7+143360 x^8\right ) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}+\left (-184+1525 x-6328 x^2-8025 x^3-1680 x^4-3740 x^5+8192 x^6+10240 x^7\right ) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}+\sqrt {1+x^2} \left (\left (-282-3314848 x+5298 x^2-3989088 x^3+7272 x^4+5789696 x^5-12288 x^6+143360 x^7\right ) \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}+\left (935-2416 x-2315 x^2-5776 x^3-8860 x^4+8192 x^5+10240 x^6\right ) \sqrt {x+\sqrt {1+x^2}} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}\right )}{40320 \left (-1+x^2\right ) \sqrt {1+x^2} \left (4 x+8 x^3\right )+40320 \left (-1+x^2\right ) \left (1+8 x^2+8 x^4\right )}-\frac {2299}{128} \tanh ^{-1}\left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}\right )+4 \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{2 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]-\frac {1}{4} \text {RootSum}\left [-2+4 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {14 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+3 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{2 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]-4 \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {-\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+\log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{-2 \text {$\#$1}+4 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ]+\frac {1}{4} \text {RootSum}\left [2-8 \text {$\#$1}^2+8 \text {$\#$1}^4-4 \text {$\#$1}^6+\text {$\#$1}^8\&,\frac {-16 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right )-2 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^2+3 \log \left (\sqrt {1+\sqrt {x+\sqrt {1+x^2}}}-\text {$\#$1}\right ) \text {$\#$1}^4}{-2 \text {$\#$1}+4 \text {$\#$1}^3-3 \text {$\#$1}^5+\text {$\#$1}^7}\&\right ] \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

IntegrateAlgebraic[((1 + x^2)^(5/2)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]])/(1 - x^2)^2,x]

[Out]

((-803792 + 690*x - 6024144*x^2 + 10470*x^3 - 1112160*x^4 + 1128*x^5 + 5861376*x^6 - 12288*x^7 + 143360*x^8)*S

qrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + (-184 + 1525*x - 6328*x^2 - 8025*x^3 - 1680*x^4 - 3740*x^5 + 8192*x^6 + 102

40*x^7)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + Sqrt[1 + x^2]*((-282 - 3314848*x + 5298*x^

2 - 3989088*x^3 + 7272*x^4 + 5789696*x^5 - 12288*x^6 + 143360*x^7)*Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] + (935 -

2416*x - 2315*x^2 - 5776*x^3 - 8860*x^4 + 8192*x^5 + 10240*x^6)*Sqrt[x + Sqrt[1 + x^2]]*Sqrt[1 + Sqrt[x + Sqrt

[1 + x^2]]]))/(40320*(-1 + x^2)*Sqrt[1 + x^2]*(4*x + 8*x^3) + 40320*(-1 + x^2)*(1 + 8*x^2 + 8*x^4)) - (2299*Ar

cTanh[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]]])/128 + 4*RootSum[-2 + 4*#1^4 - 4*#1^6 + #1^8 & , (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*#1^3 - 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) & ]/4 - 4*RootSum[2 - 8*#1^2 + 8*#1^4 - 4*#1^6 + #1^8 & , (-L

og[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1] - Log[Sqrt[1 + Sqrt[x + Sqrt[1 + x^2]]] - #1]*#1^2 + Log[Sqrt[1 + S

qrt[x + Sqrt[1 + x^2]]] - #1]*#1^4)/(-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) & ]/4

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fricas [B] time = 1.80, size = 6743, normalized size = 11.18

result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^2+1)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm="fricas")

[Out]

-1/80640*(20160*sqrt(1/2)*(x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)*log(1/4*sqrt

(1/2)*(547633*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^3 + (1095266*sqrt(1/2)*sqrt(14933*sqrt

(2) + 18583) + 547633*sqrt(2) + 820211864)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 + 31105

5544*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 - (547633*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 1

8583) + sqrt(2) - 142)^2 + 622111088*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + 311055544*sqrt(2) + 210463757752)

*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) + 51091968368*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583)

+ 25545984184*sqrt(2) - 23818438149128)*sqrt(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) + 78292

579460375*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 20160*sqrt(1/2)*(x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(14933*sqrt(2) +

18583) - sqrt(2) + 142)*log(-1/4*sqrt(1/2)*(547633*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^

3 + (1095266*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + 547633*sqrt(2) + 820211864)*(2*sqrt(1/2)*sqrt(14933*sqrt(

2) + 18583) - sqrt(2) + 142)^2 + 311055544*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 - (5476

33*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 622111088*sqrt(1/2)*sqrt(14933*sqrt(2) + 1858

3) + 311055544*sqrt(2) + 210463757752)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) + 51091968368

*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + 25545984184*sqrt(2) - 23818438149128)*sqrt(2*sqrt(1/2)*sqrt(14933*sqr

t(2) + 18583) - sqrt(2) + 142) + 78292579460375*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 20160*sqrt(1/2)*(x^2 - 1)

*sqrt(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)*log(1/4*sqrt(1/2)*((438047238*sqrt(1/2)*sqrt(14

593*sqrt(2) - 18193) - 219023619*sqrt(2) + 310702217138)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) +

144)^2 + 219023619*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^3 - (219023619*(2*sqrt(1/2)*sqrt(

14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 + 252315209088*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 126157604544*

sqrt(2) + 80733215480968)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144) + 126157604544*(2*sqrt(1/2

)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 + 86375906577792*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 4318

7953288896*sqrt(2) + 15300143559468424)*sqrt(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144) + 292828

84968104501*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 20160*sqrt(1/2)*(x^2 - 1)*sqrt(2*sqrt(1/2)*sqrt(14593*sqrt(2)

- 18193) + sqrt(2) + 144)*log(-1/4*sqrt(1/2)*((438047238*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 219023619*sq

rt(2) + 310702217138)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 + 219023619*(2*sqrt(1/2)*sqr

t(14593*sqrt(2) - 18193) - sqrt(2) - 144)^3 - (219023619*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) -

144)^2 + 252315209088*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 126157604544*sqrt(2) + 80733215480968)*(2*sqrt(1

/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144) + 126157604544*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqr

t(2) - 144)^2 + 86375906577792*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 43187953288896*sqrt(2) + 15300143559468

424)*sqrt(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144) + 29282884968104501*sqrt(sqrt(x + sqrt(x^2

+ 1)) + 1)) - 20160*(x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142

)^2 + 1/16*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583)

- sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(14933*

sqrt(2) + 18583) - 71/2*sqrt(2) + 9292) + 1/2*sqrt(2) + 71)*log(1/8*((1095266*sqrt(1/2)*sqrt(14933*sqrt(2) + 1

8583) + 547633*sqrt(2) + 820211864)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 + 897975750*(2

*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 - (547633*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) +

sqrt(2) - 142)^2 + 622111088*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + 311055544*sqrt(2) + 210463757752)*(2*sqr

t(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) + 4*sqrt(-3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) +

sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(14933*sqrt

(2) + 18583) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 - 71*sqrt(1/2

)*sqrt(14933*sqrt(2) + 18583) - 71/2*sqrt(2) + 9292)*((547633*sqrt(2)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583)

+ sqrt(2) - 142) + 897975750*sqrt(2))*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 897975750*s

qrt(2)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142) - 255416581000*sqrt(2)) + 509267290000*sqrt(1

/2)*sqrt(14933*sqrt(2) + 18583) + 254633645000*sqrt(2) - 57075233236000)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*

sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) + 426

)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) -

sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - 71/2*sqrt(2) + 9292) + 1/2*sqrt(2) + 71) + 78292

579460375*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 20160*(x^2 - 1)*sqrt(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(14933

*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) + 426)*(2*sqrt(

1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) +

142)^2 - 71*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - 71/2*sqrt(2) + 9292) + 1/2*sqrt(2) + 71)*log(-1/8*((109526

6*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + 547633*sqrt(2) + 820211864)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583)

- sqrt(2) + 142)^2 + 897975750*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 - (547633*(2*sqrt(

1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 622111088*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + 311055

544*sqrt(2) + 210463757752)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) + 4*sqrt(-3/32*(2*sqrt(1

/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) +

426)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583

) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - 71/2*sqrt(2) + 9292)*((547633*sqrt(2)*(2*sqr

t(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142) + 897975750*sqrt(2))*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 185

83) - sqrt(2) + 142) - 897975750*sqrt(2)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142) - 255416581

000*sqrt(2)) + 509267290000*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + 254633645000*sqrt(2) - 57075233236000)*sqr

t(sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(1493

3*sqrt(2) + 18583) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 3/32*(2*sqrt(1

/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - 71/2*sqrt(2) +

9292) + 1/2*sqrt(2) + 71) + 78292579460375*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 20160*(x^2 - 1)*sqrt(-sqrt(2)

*sqrt(-3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(14933*sqrt(2)

+ 18583) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(

14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - 71/2*sqrt(2) + 9292) +

1/2*sqrt(2) + 71)*log(1/8*((1095266*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + 547633*sqrt(2) + 820211864)*(2*sqr

t(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 + 897975750*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + s

qrt(2) - 142)^2 - (547633*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 622111088*sqrt(1/2)*sq

rt(14933*sqrt(2) + 18583) + 311055544*sqrt(2) + 210463757752)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(

2) + 142) - 4*sqrt(-3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(

14933*sqrt(2) + 18583) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 3/32*(2*sq

rt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - 71/2*sqrt(

2) + 9292)*((547633*sqrt(2)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142) + 897975750*sqrt(2))*(2*

sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 897975750*sqrt(2)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 1

8583) + sqrt(2) - 142) - 255416581000*sqrt(2)) + 509267290000*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + 25463364

5000*sqrt(2) - 57075233236000)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 1

42)^2 + 1/16*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583

) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(1493

3*sqrt(2) + 18583) - 71/2*sqrt(2) + 9292) + 1/2*sqrt(2) + 71) + 78292579460375*sqrt(sqrt(x + sqrt(x^2 + 1)) +

1)) + 20160*(x^2 - 1)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 1

/16*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(

2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt(14933*sqrt(2)

+ 18583) - 71/2*sqrt(2) + 9292) + 1/2*sqrt(2) + 71)*log(-1/8*((1095266*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583)

+ 547633*sqrt(2) + 820211864)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 + 897975750*(2*sqrt(

1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 - (547633*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(

2) - 142)^2 + 622111088*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + 311055544*sqrt(2) + 210463757752)*(2*sqrt(1/2)

*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 4*sqrt(-3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2

) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) + 426)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) +

18583) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142)^2 - 71*sqrt(1/2)*sqrt

(14933*sqrt(2) + 18583) - 71/2*sqrt(2) + 9292)*((547633*sqrt(2)*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqr

t(2) - 142) + 897975750*sqrt(2))*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 897975750*sqrt(2)

*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142) - 255416581000*sqrt(2)) + 509267290000*sqrt(1/2)*sq

rt(14933*sqrt(2) + 18583) + 254633645000*sqrt(2) - 57075233236000)*sqrt(-sqrt(2)*sqrt(-3/32*(2*sqrt(1/2)*sqrt(

14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 + 1/16*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) + 426)*(2*

sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(2) + 142) - 3/32*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - sqrt(

2) + 142)^2 - 71*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - 71/2*sqrt(2) + 9292) + 1/2*sqrt(2) + 71) + 7829257946

0375*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 80640*(x^2 - 1)*sqrt(-1/16*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - 1

/32*sqrt(2) + 71/16)*log((547633*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^3 - 586920206*(2*sq

rt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 - 458175321632*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) -

229087660816*sqrt(2) + 47301322903272)*sqrt(-1/16*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - 1/32*sqrt(2) + 71/16

) + 78292579460375*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 80640*(x^2 - 1)*sqrt(-1/16*sqrt(1/2)*sqrt(14933*sqrt(2

) + 18583) - 1/32*sqrt(2) + 71/16)*log(-(547633*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^3 -

586920206*(2*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) + sqrt(2) - 142)^2 - 458175321632*sqrt(1/2)*sqrt(14933*sqrt

(2) + 18583) - 229087660816*sqrt(2) + 47301322903272)*sqrt(-1/16*sqrt(1/2)*sqrt(14933*sqrt(2) + 18583) - 1/32*

sqrt(2) + 71/16) + 78292579460375*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 80640*(x^2 - 1)*sqrt(-1/16*sqrt(1/2)*sq

rt(14593*sqrt(2) - 18193) + 1/32*sqrt(2) + 9/2)*log((219023619*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt

(2) - 144)^3 - 216084013730*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 - 111423914492816*sqrt

(1/2)*sqrt(14593*sqrt(2) - 18193) + 55711957246408*sqrt(2) - 6239425231280344)*sqrt(-1/16*sqrt(1/2)*sqrt(14593

*sqrt(2) - 18193) + 1/32*sqrt(2) + 9/2) + 29282884968104501*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 80640*(x^2 -

1)*sqrt(-1/16*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 1/32*sqrt(2) + 9/2)*log(-(219023619*(2*sqrt(1/2)*sqrt(14

593*sqrt(2) - 18193) - sqrt(2) - 144)^3 - 216084013730*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 14

4)^2 - 111423914492816*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 55711957246408*sqrt(2) - 6239425231280344)*sqrt

(-1/16*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 1/32*sqrt(2) + 9/2) + 29282884968104501*sqrt(sqrt(x + sqrt(x^2

+ 1)) + 1)) + 40320*(x^2 - 1)*sqrt(-1/8*sqrt(2) + sqrt(-3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(

2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(14593*sqrt(2)

- 18193) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sq

rt(14593*sqrt(2) - 18193) + 9/2*sqrt(2) - 1137) + 18)*log(1/4*((438047238*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193

) - 219023619*sqrt(2) + 310702217138)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 - (219023619

*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 + 252315209088*sqrt(1/2)*sqrt(14593*sqrt(2) - 181

93) - 126157604544*sqrt(2) + 80733215480968)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144) + 34224

1618274*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 + 16*((438047238*sqrt(1/2)*sqrt(14593*sqrt

(2) - 18193) - 219023619*sqrt(2) + 310702217138)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144) - 6

84483236548*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 342241618274*sqrt(2) - 48948468559064)*sqrt(-3/256*(2*sqrt

(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2

) + 144)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 1

8193) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 9/2*sqrt(2) - 1137) + 197799821070608*sqr

t(1/2)*sqrt(14593*sqrt(2) - 18193) - 98899910535304*sqrt(2) + 21107931056118640)*sqrt(-1/8*sqrt(2) + sqrt(-3/2

56*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193

) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(14593*s

qrt(2) - 18193) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 9/2*sqrt(2) - 1137) + 18) + 292

82884968104501*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) - 40320*(x^2 - 1)*sqrt(-1/8*sqrt(2) + sqrt(-3/256*(2*sqrt(1/

2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) +

144)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 1819

3) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 9/2*sqrt(2) - 1137) + 18)*log(-1/4*((4380472

38*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 219023619*sqrt(2) + 310702217138)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) -

18193) + sqrt(2) + 144)^2 - (219023619*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 + 25231520

9088*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 126157604544*sqrt(2) + 80733215480968)*(2*sqrt(1/2)*sqrt(14593*sq

rt(2) - 18193) + sqrt(2) + 144) + 342241618274*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 + 1

6*((438047238*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 219023619*sqrt(2) + 310702217138)*(2*sqrt(1/2)*sqrt(1459

3*sqrt(2) - 18193) + sqrt(2) + 144) - 684483236548*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 342241618274*sqrt(2

) - 48948468559064)*sqrt(-3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/

2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) + 432) - 3/

256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 9/

2*sqrt(2) - 1137) + 197799821070608*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 98899910535304*sqrt(2) + 211079310

56118640)*sqrt(-1/8*sqrt(2) + sqrt(-3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 + 1/128*

(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) +

432) - 3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(14593*sqrt(2) - 1

8193) + 9/2*sqrt(2) - 1137) + 18) + 29282884968104501*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 40320*(x^2 - 1)*sqr

t(-1/8*sqrt(2) - sqrt(-3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*

sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) + 432) - 3/256

*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 9/2*s

qrt(2) - 1137) + 18)*log(1/4*((438047238*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 219023619*sqrt(2) + 310702217

138)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 - (219023619*(2*sqrt(1/2)*sqrt(14593*sqrt(2)

- 18193) - sqrt(2) - 144)^2 + 252315209088*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 126157604544*sqrt(2) + 8073

3215480968)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144) + 342241618274*(2*sqrt(1/2)*sqrt(14593*s

qrt(2) - 18193) - sqrt(2) - 144)^2 - 16*((438047238*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 219023619*sqrt(2)

+ 310702217138)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144) - 684483236548*sqrt(1/2)*sqrt(14593*

sqrt(2) - 18193) + 342241618274*sqrt(2) - 48948468559064)*sqrt(-3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193)

+ sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(14593*

sqrt(2) - 18193) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 - 9*sqrt

(1/2)*sqrt(14593*sqrt(2) - 18193) + 9/2*sqrt(2) - 1137) + 197799821070608*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193

) - 98899910535304*sqrt(2) + 21107931056118640)*sqrt(-1/8*sqrt(2) - sqrt(-3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2

) - 18193) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)*(2*sqrt(1/2)*s

qrt(14593*sqrt(2) - 18193) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^

2 - 9*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 9/2*sqrt(2) - 1137) + 18) + 29282884968104501*sqrt(sqrt(x + sqrt

(x^2 + 1)) + 1)) - 40320*(x^2 - 1)*sqrt(-1/8*sqrt(2) - sqrt(-3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) +

sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(14593*sqr

t(2) - 18193) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 - 9*sqrt(1/

2)*sqrt(14593*sqrt(2) - 18193) + 9/2*sqrt(2) - 1137) + 18)*log(-1/4*((438047238*sqrt(1/2)*sqrt(14593*sqrt(2) -

18193) - 219023619*sqrt(2) + 310702217138)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 - (219

023619*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 + 252315209088*sqrt(1/2)*sqrt(14593*sqrt(2)

- 18193) - 126157604544*sqrt(2) + 80733215480968)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144) +

342241618274*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) - 144)^2 - 16*((438047238*sqrt(1/2)*sqrt(1459

3*sqrt(2) - 18193) - 219023619*sqrt(2) + 310702217138)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 14

4) - 684483236548*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 342241618274*sqrt(2) - 48948468559064)*sqrt(-3/256*(

2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) +

sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(

2) - 18193) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 9/2*sqrt(2) - 1137) + 1977998210706

08*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - 98899910535304*sqrt(2) + 21107931056118640)*sqrt(-1/8*sqrt(2) - sqr

t(-3/256*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + sqrt(2) + 144)^2 + 1/128*(2*sqrt(1/2)*sqrt(14593*sqrt(2) -

18193) + sqrt(2) + 144)*(2*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) - sqrt(2) + 432) - 3/256*(2*sqrt(1/2)*sqrt(1

4593*sqrt(2) - 18193) - sqrt(2) - 144)^2 - 9*sqrt(1/2)*sqrt(14593*sqrt(2) - 18193) + 9/2*sqrt(2) - 1137) + 18)

+ 29282884968104501*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)) + 724185*(x^2 - 1)*log(sqrt(sqrt(x + sqrt(x^2 + 1)) +

1) + 1) - 724185*(x^2 - 1)*log(sqrt(sqrt(x + sqrt(x^2 + 1)) + 1) - 1) + 2*(1120*x^4 + 1818*x^3 - 804912*x^2 -

2*(9520*x^3 + 141*x^2 - 49840*x - 141)*sqrt(x^2 + 1) + (1680*x^4 - 2215*x^3 - 1864*x^2 - 5*(336*x^3 - 187*x^2

- 336*x + 187)*sqrt(x^2 + 1) + 2215*x + 184)*sqrt(x + sqrt(x^2 + 1)) - 1818*x + 803792)*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)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

maple [F] time = 0.00, size = 0, normalized size = 0.00 \[\int \frac {\left (x^{2}+1\right )^{\frac {5}{2}} \sqrt {1+\sqrt {x +\sqrt {x^{2}+1}}}}{\left (-x^{2}+1\right )^{2}}\, dx\]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((x^2+1)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)

[Out]

int((x^2+1)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x)

________________________________________________________________________________________

maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{2} + 1\right )}^{\frac {5}{2}} \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)^(5/2)*(1+(x+(x^2+1)^(1/2))^(1/2))^(1/2)/(-x^2+1)^2,x, algorithm="maxima")

[Out]

integrate((x^2 + 1)^(5/2)*sqrt(sqrt(x + sqrt(x^2 + 1)) + 1)/(x^2 - 1)^2, x)

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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {\sqrt {\sqrt {x+\sqrt {x^2+1}}+1}\,{\left (x^2+1\right )}^{5/2}}{{\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)^(5/2))/(x^2 - 1)^2,x)

[Out]

int((((x + (x^2 + 1)^(1/2))^(1/2) + 1)^(1/2)*(x^2 + 1)^(5/2))/(x^2 - 1)^2, x)

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sympy [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)**(5/2)*(1+(x+(x**2+1)**(1/2))**(1/2))**(1/2)/(-x**2+1)**2,x)

[Out]

Timed out

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3.32.7 \(\int \frac {(1+x^2)^{5/2} \sqrt {1+\sqrt {x+\sqrt {1+x^2}}}}{(1-x^2)^2} \, dx\)