Optimal. Leaf size=283 \[ -\frac {604}{1519 \sqrt {1+2 x}}+\frac {37+20 x}{217 \sqrt {1+2 x} \left (2+3 x+5 x^2\right )}+\frac {\sqrt {\frac {2}{217} \left (-5682718+968975 \sqrt {35}\right )} \tan ^{-1}\left (\frac {\sqrt {10 \left (2+\sqrt {35}\right )}-10 \sqrt {1+2 x}}{\sqrt {10 \left (-2+\sqrt {35}\right )}}\right )}{1519}-\frac {\sqrt {\frac {2}{217} \left (-5682718+968975 \sqrt {35}\right )} \tan ^{-1}\left (\frac {\sqrt {10 \left (2+\sqrt {35}\right )}+10 \sqrt {1+2 x}}{\sqrt {10 \left (-2+\sqrt {35}\right )}}\right )}{1519}-\frac {\sqrt {\frac {1}{434} \left (5682718+968975 \sqrt {35}\right )} \log \left (\sqrt {35}-\sqrt {10 \left (2+\sqrt {35}\right )} \sqrt {1+2 x}+5 (1+2 x)\right )}{1519}+\frac {\sqrt {\frac {1}{434} \left (5682718+968975 \sqrt {35}\right )} \log \left (\sqrt {35}+\sqrt {10 \left (2+\sqrt {35}\right )} \sqrt {1+2 x}+5 (1+2 x)\right )}{1519} \]
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Rubi [A]
time = 0.26, antiderivative size = 283, normalized size of antiderivative = 1.00, number of steps
used = 12, number of rules used = 8, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.364, Rules used = {754, 842, 840,
1183, 648, 632, 210, 642} \begin {gather*} \frac {\sqrt {\frac {2}{217} \left (968975 \sqrt {35}-5682718\right )} \text {ArcTan}\left (\frac {\sqrt {10 \left (2+\sqrt {35}\right )}-10 \sqrt {2 x+1}}{\sqrt {10 \left (\sqrt {35}-2\right )}}\right )}{1519}-\frac {\sqrt {\frac {2}{217} \left (968975 \sqrt {35}-5682718\right )} \text {ArcTan}\left (\frac {10 \sqrt {2 x+1}+\sqrt {10 \left (2+\sqrt {35}\right )}}{\sqrt {10 \left (\sqrt {35}-2\right )}}\right )}{1519}+\frac {20 x+37}{217 \sqrt {2 x+1} \left (5 x^2+3 x+2\right )}-\frac {604}{1519 \sqrt {2 x+1}}-\frac {\sqrt {\frac {1}{434} \left (5682718+968975 \sqrt {35}\right )} \log \left (5 (2 x+1)-\sqrt {10 \left (2+\sqrt {35}\right )} \sqrt {2 x+1}+\sqrt {35}\right )}{1519}+\frac {\sqrt {\frac {1}{434} \left (5682718+968975 \sqrt {35}\right )} \log \left (5 (2 x+1)+\sqrt {10 \left (2+\sqrt {35}\right )} \sqrt {2 x+1}+\sqrt {35}\right )}{1519} \end {gather*}
Antiderivative was successfully verified.
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Rule 210
Rule 632
Rule 642
Rule 648
Rule 754
Rule 840
Rule 842
Rule 1183
Rubi steps
\begin {align*} \int \frac {1}{(1+2 x)^{3/2} \left (2+3 x+5 x^2\right )^2} \, dx &=\frac {37+20 x}{217 \sqrt {1+2 x} \left (2+3 x+5 x^2\right )}+\frac {1}{217} \int \frac {181+60 x}{(1+2 x)^{3/2} \left (2+3 x+5 x^2\right )} \, dx\\ &=-\frac {604}{1519 \sqrt {1+2 x}}+\frac {37+20 x}{217 \sqrt {1+2 x} \left (2+3 x+5 x^2\right )}+\frac {\int \frac {59-1510 x}{\sqrt {1+2 x} \left (2+3 x+5 x^2\right )} \, dx}{1519}\\ &=-\frac {604}{1519 \sqrt {1+2 x}}+\frac {37+20 x}{217 \sqrt {1+2 x} \left (2+3 x+5 x^2\right )}+\frac {2 \text {Subst}\left (\int \frac {1628-1510 x^2}{7-4 x^2+5 x^4} \, dx,x,\sqrt {1+2 x}\right )}{1519}\\ &=-\frac {604}{1519 \sqrt {1+2 x}}+\frac {37+20 x}{217 \sqrt {1+2 x} \left (2+3 x+5 x^2\right )}+\frac {\text {Subst}\left (\int \frac {1628 \sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )}-\left (1628+302 \sqrt {35}\right ) x}{\sqrt {\frac {7}{5}}-\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )} x+x^2} \, dx,x,\sqrt {1+2 x}\right )}{1519 \sqrt {14 \left (2+\sqrt {35}\right )}}+\frac {\text {Subst}\left (\int \frac {1628 \sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )}+\left (1628+302 \sqrt {35}\right ) x}{\sqrt {\frac {7}{5}}+\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )} x+x^2} \, dx,x,\sqrt {1+2 x}\right )}{1519 \sqrt {14 \left (2+\sqrt {35}\right )}}\\ &=-\frac {604}{1519 \sqrt {1+2 x}}+\frac {37+20 x}{217 \sqrt {1+2 x} \left (2+3 x+5 x^2\right )}+\frac {\left (-5285+814 \sqrt {35}\right ) \text {Subst}\left (\int \frac {1}{\sqrt {\frac {7}{5}}-\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )} x+x^2} \, dx,x,\sqrt {1+2 x}\right )}{53165}+\frac {\left (-5285+814 \sqrt {35}\right ) \text {Subst}\left (\int \frac {1}{\sqrt {\frac {7}{5}}+\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )} x+x^2} \, dx,x,\sqrt {1+2 x}\right )}{53165}-\frac {\sqrt {\frac {1}{434} \left (5682718+968975 \sqrt {35}\right )} \text {Subst}\left (\int \frac {-\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )}+2 x}{\sqrt {\frac {7}{5}}-\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )} x+x^2} \, dx,x,\sqrt {1+2 x}\right )}{1519}+\frac {\sqrt {\frac {1}{434} \left (5682718+968975 \sqrt {35}\right )} \text {Subst}\left (\int \frac {\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )}+2 x}{\sqrt {\frac {7}{5}}+\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )} x+x^2} \, dx,x,\sqrt {1+2 x}\right )}{1519}\\ &=-\frac {604}{1519 \sqrt {1+2 x}}+\frac {37+20 x}{217 \sqrt {1+2 x} \left (2+3 x+5 x^2\right )}-\frac {\sqrt {\frac {1}{434} \left (5682718+968975 \sqrt {35}\right )} \log \left (\sqrt {35}-\sqrt {10 \left (2+\sqrt {35}\right )} \sqrt {1+2 x}+5 (1+2 x)\right )}{1519}+\frac {\sqrt {\frac {1}{434} \left (5682718+968975 \sqrt {35}\right )} \log \left (\sqrt {35}+\sqrt {10 \left (2+\sqrt {35}\right )} \sqrt {1+2 x}+5 (1+2 x)\right )}{1519}+\frac {\left (2 \left (5285-814 \sqrt {35}\right )\right ) \text {Subst}\left (\int \frac {1}{\frac {2}{5} \left (2-\sqrt {35}\right )-x^2} \, dx,x,-\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )}+2 \sqrt {1+2 x}\right )}{53165}+\frac {\left (2 \left (5285-814 \sqrt {35}\right )\right ) \text {Subst}\left (\int \frac {1}{\frac {2}{5} \left (2-\sqrt {35}\right )-x^2} \, dx,x,\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )}+2 \sqrt {1+2 x}\right )}{53165}\\ &=-\frac {604}{1519 \sqrt {1+2 x}}+\frac {37+20 x}{217 \sqrt {1+2 x} \left (2+3 x+5 x^2\right )}+\frac {\sqrt {\frac {2}{217} \left (-5682718+968975 \sqrt {35}\right )} \tan ^{-1}\left (\sqrt {\frac {5}{2 \left (-2+\sqrt {35}\right )}} \left (\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )}-2 \sqrt {1+2 x}\right )\right )}{1519}-\frac {\sqrt {\frac {2}{217} \left (-5682718+968975 \sqrt {35}\right )} \tan ^{-1}\left (\sqrt {\frac {5}{2 \left (-2+\sqrt {35}\right )}} \left (\sqrt {\frac {2}{5} \left (2+\sqrt {35}\right )}+2 \sqrt {1+2 x}\right )\right )}{1519}-\frac {\sqrt {\frac {1}{434} \left (5682718+968975 \sqrt {35}\right )} \log \left (\sqrt {35}-\sqrt {10 \left (2+\sqrt {35}\right )} \sqrt {1+2 x}+5 (1+2 x)\right )}{1519}+\frac {\sqrt {\frac {1}{434} \left (5682718+968975 \sqrt {35}\right )} \log \left (\sqrt {35}+\sqrt {10 \left (2+\sqrt {35}\right )} \sqrt {1+2 x}+5 (1+2 x)\right )}{1519}\\ \end {align*}
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Mathematica [C] Result contains complex when optimal does not.
time = 1.13, size = 138, normalized size = 0.49 \begin {gather*} \frac {2 \left (-\frac {217 \left (949+1672 x+3020 x^2\right )}{2 \sqrt {1+2 x} \left (2+3 x+5 x^2\right )}-\sqrt {217 \left (-5682718-135439 i \sqrt {31}\right )} \tan ^{-1}\left (\sqrt {\frac {1}{7} \left (-2-i \sqrt {31}\right )} \sqrt {1+2 x}\right )-\sqrt {217 \left (-5682718+135439 i \sqrt {31}\right )} \tan ^{-1}\left (\sqrt {\frac {1}{7} i \left (2 i+\sqrt {31}\right )} \sqrt {1+2 x}\right )\right )}{329623} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(423\) vs.
\(2(193)=386\).
time = 2.22, size = 424, normalized size = 1.50 Too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 576 vs.
\(2 (196) = 392\).
time = 2.15, size = 576, normalized size = 2.04 \begin {gather*} \frac {16794436 \cdot 21898835^{\frac {1}{4}} \sqrt {217} \sqrt {35} {\left (10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right )} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} \arctan \left (\frac {1}{84465779527115502604115125} \cdot 21898835^{\frac {3}{4}} \sqrt {4369} \sqrt {791} \sqrt {217} \sqrt {21898835^{\frac {1}{4}} \sqrt {217} {\left (151 \, \sqrt {35} \sqrt {31} + 814 \, \sqrt {31}\right )} \sqrt {2 \, x + 1} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} + 8136694311550 \, x + 813669431155 \, \sqrt {35} + 4068347155775} {\left (814 \, \sqrt {35} + 5285\right )} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} - \frac {1}{22526438201526175} \cdot 21898835^{\frac {3}{4}} \sqrt {217} \sqrt {2 \, x + 1} {\left (814 \, \sqrt {35} + 5285\right )} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} - \frac {1}{31} \, \sqrt {35} \sqrt {31} - \frac {2}{31} \, \sqrt {31}\right ) + 16794436 \cdot 21898835^{\frac {1}{4}} \sqrt {217} \sqrt {35} {\left (10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right )} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} \arctan \left (\frac {1}{206941159841432981380082056250} \cdot 21898835^{\frac {3}{4}} \sqrt {4369} \sqrt {217} \sqrt {-4747977500 \cdot 21898835^{\frac {1}{4}} \sqrt {217} {\left (151 \, \sqrt {35} \sqrt {31} + 814 \, \sqrt {31}\right )} \sqrt {2 \, x + 1} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} + 38632841515617390125000 \, x + 3863284151561739012500 \, \sqrt {35} + 19316420757808695062500} {\left (814 \, \sqrt {35} + 5285\right )} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} - \frac {1}{22526438201526175} \cdot 21898835^{\frac {3}{4}} \sqrt {217} \sqrt {2 \, x + 1} {\left (814 \, \sqrt {35} + 5285\right )} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} + \frac {1}{31} \, \sqrt {35} \sqrt {31} + \frac {2}{31} \, \sqrt {31}\right ) + 21898835^{\frac {1}{4}} \sqrt {217} {\left (5682718 \, \sqrt {35} \sqrt {31} {\left (10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right )} + 33914125 \, \sqrt {31} {\left (10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right )}\right )} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} \log \left (\frac {4747977500}{4369} \cdot 21898835^{\frac {1}{4}} \sqrt {217} {\left (151 \, \sqrt {35} \sqrt {31} + 814 \, \sqrt {31}\right )} \sqrt {2 \, x + 1} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} + 8842490619276125000 \, x + 884249061927612500 \, \sqrt {35} + 4421245309638062500\right ) - 21898835^{\frac {1}{4}} \sqrt {217} {\left (5682718 \, \sqrt {35} \sqrt {31} {\left (10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right )} + 33914125 \, \sqrt {31} {\left (10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right )}\right )} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} \log \left (-\frac {4747977500}{4369} \cdot 21898835^{\frac {1}{4}} \sqrt {217} {\left (151 \, \sqrt {35} \sqrt {31} + 814 \, \sqrt {31}\right )} \sqrt {2 \, x + 1} \sqrt {-11012823348100 \, \sqrt {35} + 65723878543750} + 8842490619276125000 \, x + 884249061927612500 \, \sqrt {35} + 4421245309638062500\right ) - 1765662665606350 \, {\left (3020 \, x^{2} + 1672 \, x + 949\right )} \sqrt {2 \, x + 1}}{2682041589056045650 \, {\left (10 \, x^{3} + 11 \, x^{2} + 7 \, x + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (2 x + 1\right )^{\frac {3}{2}} \left (5 x^{2} + 3 x + 2\right )^{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 633 vs.
\(2 (196) = 392\).
time = 1.52, size = 633, normalized size = 2.24 \begin {gather*} -\frac {1}{11306068900} \, \sqrt {31} {\left (31710 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (2 \, \sqrt {35} + 35\right )} \sqrt {-140 \, \sqrt {35} + 2450} - 151 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (-140 \, \sqrt {35} + 2450\right )}^{\frac {3}{2}} + 302 \, \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (140 \, \sqrt {35} + 2450\right )}^{\frac {3}{2}} + 63420 \, \left (\frac {7}{5}\right )^{\frac {3}{4}} \sqrt {140 \, \sqrt {35} + 2450} {\left (2 \, \sqrt {35} - 35\right )} - 797720 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {-140 \, \sqrt {35} + 2450} - 1595440 \, \left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {140 \, \sqrt {35} + 2450}\right )} \arctan \left (\frac {5 \, \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (\left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {\frac {1}{35} \, \sqrt {35} + \frac {1}{2}} + \sqrt {2 \, x + 1}\right )}}{7 \, \sqrt {-\frac {1}{35} \, \sqrt {35} + \frac {1}{2}}}\right ) - \frac {1}{11306068900} \, \sqrt {31} {\left (31710 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (2 \, \sqrt {35} + 35\right )} \sqrt {-140 \, \sqrt {35} + 2450} - 151 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (-140 \, \sqrt {35} + 2450\right )}^{\frac {3}{2}} + 302 \, \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (140 \, \sqrt {35} + 2450\right )}^{\frac {3}{2}} + 63420 \, \left (\frac {7}{5}\right )^{\frac {3}{4}} \sqrt {140 \, \sqrt {35} + 2450} {\left (2 \, \sqrt {35} - 35\right )} - 797720 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {-140 \, \sqrt {35} + 2450} - 1595440 \, \left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {140 \, \sqrt {35} + 2450}\right )} \arctan \left (-\frac {5 \, \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (\left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {\frac {1}{35} \, \sqrt {35} + \frac {1}{2}} - \sqrt {2 \, x + 1}\right )}}{7 \, \sqrt {-\frac {1}{35} \, \sqrt {35} + \frac {1}{2}}}\right ) - \frac {1}{22612137800} \, \sqrt {31} {\left (151 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (140 \, \sqrt {35} + 2450\right )}^{\frac {3}{2}} + 31710 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {3}{4}} \sqrt {140 \, \sqrt {35} + 2450} {\left (2 \, \sqrt {35} - 35\right )} - 63420 \, \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (2 \, \sqrt {35} + 35\right )} \sqrt {-140 \, \sqrt {35} + 2450} + 302 \, \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (-140 \, \sqrt {35} + 2450\right )}^{\frac {3}{2}} - 797720 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {140 \, \sqrt {35} + 2450} + 1595440 \, \left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {-140 \, \sqrt {35} + 2450}\right )} \log \left (2 \, \left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {2 \, x + 1} \sqrt {\frac {1}{35} \, \sqrt {35} + \frac {1}{2}} + 2 \, x + \sqrt {\frac {7}{5}} + 1\right ) + \frac {1}{22612137800} \, \sqrt {31} {\left (151 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (140 \, \sqrt {35} + 2450\right )}^{\frac {3}{2}} + 31710 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {3}{4}} \sqrt {140 \, \sqrt {35} + 2450} {\left (2 \, \sqrt {35} - 35\right )} - 63420 \, \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (2 \, \sqrt {35} + 35\right )} \sqrt {-140 \, \sqrt {35} + 2450} + 302 \, \left (\frac {7}{5}\right )^{\frac {3}{4}} {\left (-140 \, \sqrt {35} + 2450\right )}^{\frac {3}{2}} - 797720 \, \sqrt {31} \left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {140 \, \sqrt {35} + 2450} + 1595440 \, \left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {-140 \, \sqrt {35} + 2450}\right )} \log \left (-2 \, \left (\frac {7}{5}\right )^{\frac {1}{4}} \sqrt {2 \, x + 1} \sqrt {\frac {1}{35} \, \sqrt {35} + \frac {1}{2}} + 2 \, x + \sqrt {\frac {7}{5}} + 1\right ) - \frac {4 \, {\left (755 \, {\left (2 \, x + 1\right )}^{2} - 1348 \, x + 194\right )}}{1519 \, {\left (5 \, {\left (2 \, x + 1\right )}^{\frac {5}{2}} - 4 \, {\left (2 \, x + 1\right )}^{\frac {3}{2}} + 7 \, \sqrt {2 \, x + 1}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.04, size = 217, normalized size = 0.77 \begin {gather*} -\frac {\frac {604\,{\left (2\,x+1\right )}^2}{1519}-\frac {5392\,x}{7595}+\frac {776}{7595}}{\frac {7\,\sqrt {2\,x+1}}{5}-\frac {4\,{\left (2\,x+1\right )}^{3/2}}{5}+{\left (2\,x+1\right )}^{5/2}}-\frac {\sqrt {217}\,\mathrm {atan}\left (\frac {\sqrt {217}\,\sqrt {5682718-\sqrt {31}\,135439{}\mathrm {i}}\,\sqrt {2\,x+1}\,559232{}\mathrm {i}}{692496720125\,\left (\frac {2045111424}{98928102875}+\frac {\sqrt {31}\,455214848{}\mathrm {i}}{98928102875}\right )}-\frac {1118464\,\sqrt {31}\,\sqrt {217}\,\sqrt {5682718-\sqrt {31}\,135439{}\mathrm {i}}\,\sqrt {2\,x+1}}{21467398323875\,\left (\frac {2045111424}{98928102875}+\frac {\sqrt {31}\,455214848{}\mathrm {i}}{98928102875}\right )}\right )\,\sqrt {5682718-\sqrt {31}\,135439{}\mathrm {i}}\,2{}\mathrm {i}}{329623}+\frac {\sqrt {217}\,\mathrm {atan}\left (\frac {\sqrt {217}\,\sqrt {5682718+\sqrt {31}\,135439{}\mathrm {i}}\,\sqrt {2\,x+1}\,559232{}\mathrm {i}}{692496720125\,\left (-\frac {2045111424}{98928102875}+\frac {\sqrt {31}\,455214848{}\mathrm {i}}{98928102875}\right )}+\frac {1118464\,\sqrt {31}\,\sqrt {217}\,\sqrt {5682718+\sqrt {31}\,135439{}\mathrm {i}}\,\sqrt {2\,x+1}}{21467398323875\,\left (-\frac {2045111424}{98928102875}+\frac {\sqrt {31}\,455214848{}\mathrm {i}}{98928102875}\right )}\right )\,\sqrt {5682718+\sqrt {31}\,135439{}\mathrm {i}}\,2{}\mathrm {i}}{329623} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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