Optimal. Leaf size=248 \[ \frac {5 x^7}{7}-\frac {17 x^5}{5}+\frac {19 x^3}{3}-\frac {1}{32} \sqrt {\frac {1}{2} \left (618291 \sqrt {3}-262771\right )} \log \left (x^2-\sqrt {2 \left (\sqrt {3}-1\right )} x+\sqrt {3}\right )+\frac {1}{32} \sqrt {\frac {1}{2} \left (618291 \sqrt {3}-262771\right )} \log \left (x^2+\sqrt {2 \left (\sqrt {3}-1\right )} x+\sqrt {3}\right )+\frac {25 \left (5 x^2+3\right ) x}{8 \left (x^4+2 x^2+3\right )}+38 x+\frac {1}{16} \sqrt {\frac {1}{2} \left (262771+618291 \sqrt {3}\right )} \tan ^{-1}\left (\frac {\sqrt {2 \left (\sqrt {3}-1\right )}-2 x}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right )-\frac {1}{16} \sqrt {\frac {1}{2} \left (262771+618291 \sqrt {3}\right )} \tan ^{-1}\left (\frac {2 x+\sqrt {2 \left (\sqrt {3}-1\right )}}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.34, antiderivative size = 248, normalized size of antiderivative = 1.00, number of steps used = 12, number of rules used = 7, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.226, Rules used = {1668, 1676, 1169, 634, 618, 204, 628} \[ \frac {5 x^7}{7}-\frac {17 x^5}{5}+\frac {19 x^3}{3}+\frac {25 \left (5 x^2+3\right ) x}{8 \left (x^4+2 x^2+3\right )}-\frac {1}{32} \sqrt {\frac {1}{2} \left (618291 \sqrt {3}-262771\right )} \log \left (x^2-\sqrt {2 \left (\sqrt {3}-1\right )} x+\sqrt {3}\right )+\frac {1}{32} \sqrt {\frac {1}{2} \left (618291 \sqrt {3}-262771\right )} \log \left (x^2+\sqrt {2 \left (\sqrt {3}-1\right )} x+\sqrt {3}\right )+38 x+\frac {1}{16} \sqrt {\frac {1}{2} \left (262771+618291 \sqrt {3}\right )} \tan ^{-1}\left (\frac {\sqrt {2 \left (\sqrt {3}-1\right )}-2 x}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right )-\frac {1}{16} \sqrt {\frac {1}{2} \left (262771+618291 \sqrt {3}\right )} \tan ^{-1}\left (\frac {2 x+\sqrt {2 \left (\sqrt {3}-1\right )}}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 204
Rule 618
Rule 628
Rule 634
Rule 1169
Rule 1668
Rule 1676
Rubi steps
\begin {align*} \int \frac {x^8 \left (4+x^2+3 x^4+5 x^6\right )}{\left (3+2 x^2+x^4\right )^2} \, dx &=\frac {25 x \left (3+5 x^2\right )}{8 \left (3+2 x^2+x^4\right )}+\frac {1}{48} \int \frac {-450-1650 x^2+1200 x^4-336 x^8+240 x^{10}}{3+2 x^2+x^4} \, dx\\ &=\frac {25 x \left (3+5 x^2\right )}{8 \left (3+2 x^2+x^4\right )}+\frac {1}{48} \int \left (1824+912 x^2-816 x^4+240 x^6-\frac {6 \left (987+1339 x^2\right )}{3+2 x^2+x^4}\right ) \, dx\\ &=38 x+\frac {19 x^3}{3}-\frac {17 x^5}{5}+\frac {5 x^7}{7}+\frac {25 x \left (3+5 x^2\right )}{8 \left (3+2 x^2+x^4\right )}-\frac {1}{8} \int \frac {987+1339 x^2}{3+2 x^2+x^4} \, dx\\ &=38 x+\frac {19 x^3}{3}-\frac {17 x^5}{5}+\frac {5 x^7}{7}+\frac {25 x \left (3+5 x^2\right )}{8 \left (3+2 x^2+x^4\right )}-\frac {\int \frac {987 \sqrt {2 \left (-1+\sqrt {3}\right )}-\left (987-1339 \sqrt {3}\right ) x}{\sqrt {3}-\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx}{16 \sqrt {6 \left (-1+\sqrt {3}\right )}}-\frac {\int \frac {987 \sqrt {2 \left (-1+\sqrt {3}\right )}+\left (987-1339 \sqrt {3}\right ) x}{\sqrt {3}+\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx}{16 \sqrt {6 \left (-1+\sqrt {3}\right )}}\\ &=38 x+\frac {19 x^3}{3}-\frac {17 x^5}{5}+\frac {5 x^7}{7}+\frac {25 x \left (3+5 x^2\right )}{8 \left (3+2 x^2+x^4\right )}-\frac {1}{32} \left (1339+329 \sqrt {3}\right ) \int \frac {1}{\sqrt {3}-\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx-\frac {1}{32} \left (1339+329 \sqrt {3}\right ) \int \frac {1}{\sqrt {3}+\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx-\frac {1}{32} \sqrt {\frac {1}{2} \left (-262771+618291 \sqrt {3}\right )} \int \frac {-\sqrt {2 \left (-1+\sqrt {3}\right )}+2 x}{\sqrt {3}-\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx+\frac {1}{32} \sqrt {\frac {1}{2} \left (-262771+618291 \sqrt {3}\right )} \int \frac {\sqrt {2 \left (-1+\sqrt {3}\right )}+2 x}{\sqrt {3}+\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2} \, dx\\ &=38 x+\frac {19 x^3}{3}-\frac {17 x^5}{5}+\frac {5 x^7}{7}+\frac {25 x \left (3+5 x^2\right )}{8 \left (3+2 x^2+x^4\right )}-\frac {1}{32} \sqrt {\frac {1}{2} \left (-262771+618291 \sqrt {3}\right )} \log \left (\sqrt {3}-\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2\right )+\frac {1}{32} \sqrt {\frac {1}{2} \left (-262771+618291 \sqrt {3}\right )} \log \left (\sqrt {3}+\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2\right )-\frac {1}{16} \left (-1339-329 \sqrt {3}\right ) \operatorname {Subst}\left (\int \frac {1}{-2 \left (1+\sqrt {3}\right )-x^2} \, dx,x,-\sqrt {2 \left (-1+\sqrt {3}\right )}+2 x\right )-\frac {1}{16} \left (-1339-329 \sqrt {3}\right ) \operatorname {Subst}\left (\int \frac {1}{-2 \left (1+\sqrt {3}\right )-x^2} \, dx,x,\sqrt {2 \left (-1+\sqrt {3}\right )}+2 x\right )\\ &=38 x+\frac {19 x^3}{3}-\frac {17 x^5}{5}+\frac {5 x^7}{7}+\frac {25 x \left (3+5 x^2\right )}{8 \left (3+2 x^2+x^4\right )}+\frac {1}{16} \sqrt {\frac {1}{2} \left (262771+618291 \sqrt {3}\right )} \tan ^{-1}\left (\frac {\sqrt {2 \left (-1+\sqrt {3}\right )}-2 x}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right )-\frac {1}{16} \sqrt {\frac {1}{2} \left (262771+618291 \sqrt {3}\right )} \tan ^{-1}\left (\frac {\sqrt {2 \left (-1+\sqrt {3}\right )}+2 x}{\sqrt {2 \left (1+\sqrt {3}\right )}}\right )-\frac {1}{32} \sqrt {\frac {1}{2} \left (-262771+618291 \sqrt {3}\right )} \log \left (\sqrt {3}-\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2\right )+\frac {1}{32} \sqrt {\frac {1}{2} \left (-262771+618291 \sqrt {3}\right )} \log \left (\sqrt {3}+\sqrt {2 \left (-1+\sqrt {3}\right )} x+x^2\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [C] time = 0.17, size = 145, normalized size = 0.58 \[ \frac {5 x^7}{7}-\frac {17 x^5}{5}+\frac {19 x^3}{3}+\frac {25 \left (5 x^2+3\right ) x}{8 \left (x^4+2 x^2+3\right )}+38 x-\frac {\left (1339 \sqrt {2}+352 i\right ) \tan ^{-1}\left (\frac {x}{\sqrt {1-i \sqrt {2}}}\right )}{16 \sqrt {2-2 i \sqrt {2}}}-\frac {\left (1339 \sqrt {2}-352 i\right ) \tan ^{-1}\left (\frac {x}{\sqrt {1+i \sqrt {2}}}\right )}{16 \sqrt {2+2 i \sqrt {2}}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.81, size = 519, normalized size = 2.09 \[ \frac {242072962564800 \, x^{11} - 668121376678848 \, x^{9} + 568064552152064 \, x^{7} + 13714240239171136 \, x^{5} - 102773860 \cdot 14158657803^{\frac {1}{4}} \sqrt {68699} \sqrt {3} \sqrt {2} {\left (x^{4} + 2 \, x^{2} + 3\right )} \sqrt {262771 \, \sqrt {3} + 1854873} \arctan \left (\frac {1}{3145089554732313026311937382} \, \sqrt {50431867201} 14158657803^{\frac {3}{4}} \sqrt {68699} \sqrt {3 \cdot 14158657803^{\frac {1}{4}} \sqrt {68699} {\left (1339 \, \sqrt {3} x - 987 \, x\right )} \sqrt {262771 \, \sqrt {3} + 1854873} + 453886804809 \, x^{2} + 453886804809 \, \sqrt {3}} {\left (329 \, \sqrt {3} \sqrt {2} - 1339 \, \sqrt {2}\right )} \sqrt {262771 \, \sqrt {3} + 1854873} - \frac {1}{20787713069048994} \cdot 14158657803^{\frac {3}{4}} \sqrt {68699} {\left (329 \, \sqrt {3} \sqrt {2} x - 1339 \, \sqrt {2} x\right )} \sqrt {262771 \, \sqrt {3} + 1854873} + \frac {1}{2} \, \sqrt {3} \sqrt {2} - \frac {1}{2} \, \sqrt {2}\right ) - 102773860 \cdot 14158657803^{\frac {1}{4}} \sqrt {68699} \sqrt {3} \sqrt {2} {\left (x^{4} + 2 \, x^{2} + 3\right )} \sqrt {262771 \, \sqrt {3} + 1854873} \arctan \left (\frac {1}{3145089554732313026311937382} \, \sqrt {50431867201} 14158657803^{\frac {3}{4}} \sqrt {68699} \sqrt {-3 \cdot 14158657803^{\frac {1}{4}} \sqrt {68699} {\left (1339 \, \sqrt {3} x - 987 \, x\right )} \sqrt {262771 \, \sqrt {3} + 1854873} + 453886804809 \, x^{2} + 453886804809 \, \sqrt {3}} {\left (329 \, \sqrt {3} \sqrt {2} - 1339 \, \sqrt {2}\right )} \sqrt {262771 \, \sqrt {3} + 1854873} - \frac {1}{20787713069048994} \cdot 14158657803^{\frac {3}{4}} \sqrt {68699} {\left (329 \, \sqrt {3} \sqrt {2} x - 1339 \, \sqrt {2} x\right )} \sqrt {262771 \, \sqrt {3} + 1854873} - \frac {1}{2} \, \sqrt {3} \sqrt {2} + \frac {1}{2} \, \sqrt {2}\right ) + 35 \cdot 14158657803^{\frac {1}{4}} \sqrt {68699} {\left (1854873 \, x^{4} + 3709746 \, x^{2} - 262771 \, \sqrt {3} {\left (x^{4} + 2 \, x^{2} + 3\right )} + 5564619\right )} \sqrt {262771 \, \sqrt {3} + 1854873} \log \left (3 \cdot 14158657803^{\frac {1}{4}} \sqrt {68699} {\left (1339 \, \sqrt {3} x - 987 \, x\right )} \sqrt {262771 \, \sqrt {3} + 1854873} + 453886804809 \, x^{2} + 453886804809 \, \sqrt {3}\right ) - 35 \cdot 14158657803^{\frac {1}{4}} \sqrt {68699} {\left (1854873 \, x^{4} + 3709746 \, x^{2} - 262771 \, \sqrt {3} {\left (x^{4} + 2 \, x^{2} + 3\right )} + 5564619\right )} \sqrt {262771 \, \sqrt {3} + 1854873} \log \left (-3 \cdot 14158657803^{\frac {1}{4}} \sqrt {68699} {\left (1339 \, \sqrt {3} x - 987 \, x\right )} \sqrt {262771 \, \sqrt {3} + 1854873} + 453886804809 \, x^{2} + 453886804809 \, \sqrt {3}\right ) + 37491050077223400 \, x^{3} + 41812052459005080 \, x}{338902147590720 \, {\left (x^{4} + 2 \, x^{2} + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 1.89, size = 585, normalized size = 2.36 \[ \frac {5}{7} \, x^{7} - \frac {17}{5} \, x^{5} + \frac {19}{3} \, x^{3} + \frac {1}{20736} \, \sqrt {2} {\left (1339 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 24102 \cdot 3^{\frac {3}{4}} \sqrt {2} \sqrt {6 \, \sqrt {3} + 18} {\left (\sqrt {3} - 3\right )} - 24102 \cdot 3^{\frac {3}{4}} {\left (\sqrt {3} + 3\right )} \sqrt {-6 \, \sqrt {3} + 18} + 1339 \cdot 3^{\frac {3}{4}} {\left (-6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} - 35532 \cdot 3^{\frac {1}{4}} \sqrt {2} \sqrt {6 \, \sqrt {3} + 18} + 35532 \cdot 3^{\frac {1}{4}} \sqrt {-6 \, \sqrt {3} + 18}\right )} \arctan \left (\frac {3^{\frac {3}{4}} {\left (x + 3^{\frac {1}{4}} \sqrt {-\frac {1}{6} \, \sqrt {3} + \frac {1}{2}}\right )}}{3 \, \sqrt {\frac {1}{6} \, \sqrt {3} + \frac {1}{2}}}\right ) + \frac {1}{20736} \, \sqrt {2} {\left (1339 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 24102 \cdot 3^{\frac {3}{4}} \sqrt {2} \sqrt {6 \, \sqrt {3} + 18} {\left (\sqrt {3} - 3\right )} - 24102 \cdot 3^{\frac {3}{4}} {\left (\sqrt {3} + 3\right )} \sqrt {-6 \, \sqrt {3} + 18} + 1339 \cdot 3^{\frac {3}{4}} {\left (-6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} - 35532 \cdot 3^{\frac {1}{4}} \sqrt {2} \sqrt {6 \, \sqrt {3} + 18} + 35532 \cdot 3^{\frac {1}{4}} \sqrt {-6 \, \sqrt {3} + 18}\right )} \arctan \left (\frac {3^{\frac {3}{4}} {\left (x - 3^{\frac {1}{4}} \sqrt {-\frac {1}{6} \, \sqrt {3} + \frac {1}{2}}\right )}}{3 \, \sqrt {\frac {1}{6} \, \sqrt {3} + \frac {1}{2}}}\right ) + \frac {1}{41472} \, \sqrt {2} {\left (24102 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (\sqrt {3} + 3\right )} \sqrt {-6 \, \sqrt {3} + 18} - 1339 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (-6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 1339 \cdot 3^{\frac {3}{4}} {\left (6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 24102 \cdot 3^{\frac {3}{4}} \sqrt {6 \, \sqrt {3} + 18} {\left (\sqrt {3} - 3\right )} - 35532 \cdot 3^{\frac {1}{4}} \sqrt {2} \sqrt {-6 \, \sqrt {3} + 18} - 35532 \cdot 3^{\frac {1}{4}} \sqrt {6 \, \sqrt {3} + 18}\right )} \log \left (x^{2} + 2 \cdot 3^{\frac {1}{4}} x \sqrt {-\frac {1}{6} \, \sqrt {3} + \frac {1}{2}} + \sqrt {3}\right ) - \frac {1}{41472} \, \sqrt {2} {\left (24102 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (\sqrt {3} + 3\right )} \sqrt {-6 \, \sqrt {3} + 18} - 1339 \cdot 3^{\frac {3}{4}} \sqrt {2} {\left (-6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 1339 \cdot 3^{\frac {3}{4}} {\left (6 \, \sqrt {3} + 18\right )}^{\frac {3}{2}} + 24102 \cdot 3^{\frac {3}{4}} \sqrt {6 \, \sqrt {3} + 18} {\left (\sqrt {3} - 3\right )} - 35532 \cdot 3^{\frac {1}{4}} \sqrt {2} \sqrt {-6 \, \sqrt {3} + 18} - 35532 \cdot 3^{\frac {1}{4}} \sqrt {6 \, \sqrt {3} + 18}\right )} \log \left (x^{2} - 2 \cdot 3^{\frac {1}{4}} x \sqrt {-\frac {1}{6} \, \sqrt {3} + \frac {1}{2}} + \sqrt {3}\right ) + 38 \, x + \frac {25 \, {\left (5 \, x^{3} + 3 \, x\right )}}{8 \, {\left (x^{4} + 2 \, x^{2} + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [B] time = 0.12, size = 427, normalized size = 1.72 \[ \frac {5 x^{7}}{7}-\frac {17 x^{5}}{5}+\frac {19 x^{3}}{3}+38 x -\frac {505 \left (-2+2 \sqrt {3}\right ) \sqrt {3}\, \arctan \left (\frac {2 x -\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{32 \sqrt {2+2 \sqrt {3}}}-\frac {11 \left (-2+2 \sqrt {3}\right ) \arctan \left (\frac {2 x -\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{2 \sqrt {2+2 \sqrt {3}}}-\frac {329 \sqrt {3}\, \arctan \left (\frac {2 x -\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{8 \sqrt {2+2 \sqrt {3}}}-\frac {505 \left (-2+2 \sqrt {3}\right ) \sqrt {3}\, \arctan \left (\frac {2 x +\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{32 \sqrt {2+2 \sqrt {3}}}-\frac {11 \left (-2+2 \sqrt {3}\right ) \arctan \left (\frac {2 x +\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{2 \sqrt {2+2 \sqrt {3}}}-\frac {329 \sqrt {3}\, \arctan \left (\frac {2 x +\sqrt {-2+2 \sqrt {3}}}{\sqrt {2+2 \sqrt {3}}}\right )}{8 \sqrt {2+2 \sqrt {3}}}-\frac {505 \sqrt {-2+2 \sqrt {3}}\, \sqrt {3}\, \ln \left (x^{2}-\sqrt {-2+2 \sqrt {3}}\, x +\sqrt {3}\right )}{64}-\frac {11 \sqrt {-2+2 \sqrt {3}}\, \ln \left (x^{2}-\sqrt {-2+2 \sqrt {3}}\, x +\sqrt {3}\right )}{4}+\frac {505 \sqrt {-2+2 \sqrt {3}}\, \sqrt {3}\, \ln \left (x^{2}+\sqrt {-2+2 \sqrt {3}}\, x +\sqrt {3}\right )}{64}+\frac {11 \sqrt {-2+2 \sqrt {3}}\, \ln \left (x^{2}+\sqrt {-2+2 \sqrt {3}}\, x +\sqrt {3}\right )}{4}-\frac {-\frac {125}{8} x^{3}-\frac {75}{8} x}{x^{4}+2 x^{2}+3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {5}{7} \, x^{7} - \frac {17}{5} \, x^{5} + \frac {19}{3} \, x^{3} + 38 \, x + \frac {25 \, {\left (5 \, x^{3} + 3 \, x\right )}}{8 \, {\left (x^{4} + 2 \, x^{2} + 3\right )}} - \frac {1}{8} \, \int \frac {1339 \, x^{2} + 987}{x^{4} + 2 \, x^{2} + 3}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.11, size = 171, normalized size = 0.69 \[ 38\,x+\frac {\frac {125\,x^3}{8}+\frac {75\,x}{8}}{x^4+2\,x^2+3}+\frac {19\,x^3}{3}-\frac {17\,x^5}{5}+\frac {5\,x^7}{7}+\frac {\mathrm {atan}\left (\frac {x\,\sqrt {-262771-\sqrt {2}\,734099{}\mathrm {i}}\,734099{}\mathrm {i}}{64\,\left (-\frac {1112159985}{64}+\frac {\sqrt {2}\,724555713{}\mathrm {i}}{128}\right )}+\frac {734099\,\sqrt {2}\,x\,\sqrt {-262771-\sqrt {2}\,734099{}\mathrm {i}}}{128\,\left (-\frac {1112159985}{64}+\frac {\sqrt {2}\,724555713{}\mathrm {i}}{128}\right )}\right )\,\sqrt {-262771-\sqrt {2}\,734099{}\mathrm {i}}\,1{}\mathrm {i}}{16}-\frac {\mathrm {atan}\left (\frac {x\,\sqrt {-262771+\sqrt {2}\,734099{}\mathrm {i}}\,734099{}\mathrm {i}}{64\,\left (\frac {1112159985}{64}+\frac {\sqrt {2}\,724555713{}\mathrm {i}}{128}\right )}-\frac {734099\,\sqrt {2}\,x\,\sqrt {-262771+\sqrt {2}\,734099{}\mathrm {i}}}{128\,\left (\frac {1112159985}{64}+\frac {\sqrt {2}\,724555713{}\mathrm {i}}{128}\right )}\right )\,\sqrt {-262771+\sqrt {2}\,734099{}\mathrm {i}}\,1{}\mathrm {i}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.61, size = 71, normalized size = 0.29 \[ \frac {5 x^{7}}{7} - \frac {17 x^{5}}{5} + \frac {19 x^{3}}{3} + 38 x + \frac {125 x^{3} + 75 x}{8 x^{4} + 16 x^{2} + 24} + \operatorname {RootSum} {\left (1048576 t^{4} + 538155008 t^{2} + 1146851282043, \left (t \mapsto t \log {\left (- \frac {16547840 t^{3}}{453886804809} - \frac {11974973632 t}{453886804809} + x \right )} \right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________