Optimal. Leaf size=197 \[ \frac {2 (21+22 x)}{15 \left (1+3 x+2 x^2\right )^{3/2}}+\frac {2 (273+230 x)}{15 \sqrt {1+3 x+2 x^2}}-\frac {1}{50} \sqrt {\frac {1}{3} \left (4885115+1544809 \sqrt {10}\right )} \tanh ^{-1}\left (\frac {3 \left (4-\sqrt {10}\right )+\left (17-4 \sqrt {10}\right ) x}{2 \sqrt {55-17 \sqrt {10}} \sqrt {1+3 x+2 x^2}}\right )+\frac {1}{50} \sqrt {\frac {1}{3} \left (4885115-1544809 \sqrt {10}\right )} \tanh ^{-1}\left (\frac {3 \left (4+\sqrt {10}\right )+\left (17+4 \sqrt {10}\right ) x}{2 \sqrt {55+17 \sqrt {10}} \sqrt {1+3 x+2 x^2}}\right ) \]
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Rubi [A]
time = 0.18, antiderivative size = 197, normalized size of antiderivative = 1.00, number of steps
used = 7, number of rules used = 5, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {1030, 1074,
1046, 738, 212} \begin {gather*} \frac {2 (22 x+21)}{15 \left (2 x^2+3 x+1\right )^{3/2}}+\frac {2 (230 x+273)}{15 \sqrt {2 x^2+3 x+1}}-\frac {1}{50} \sqrt {\frac {1}{3} \left (4885115+1544809 \sqrt {10}\right )} \tanh ^{-1}\left (\frac {\left (17-4 \sqrt {10}\right ) x+3 \left (4-\sqrt {10}\right )}{2 \sqrt {55-17 \sqrt {10}} \sqrt {2 x^2+3 x+1}}\right )+\frac {1}{50} \sqrt {\frac {1}{3} \left (4885115-1544809 \sqrt {10}\right )} \tanh ^{-1}\left (\frac {\left (17+4 \sqrt {10}\right ) x+3 \left (4+\sqrt {10}\right )}{2 \sqrt {55+17 \sqrt {10}} \sqrt {2 x^2+3 x+1}}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 212
Rule 738
Rule 1030
Rule 1046
Rule 1074
Rubi steps
\begin {align*} \int \frac {2+x}{\left (2+4 x-3 x^2\right ) \left (1+3 x+2 x^2\right )^{5/2}} \, dx &=\frac {2 (21+22 x)}{15 \left (1+3 x+2 x^2\right )^{3/2}}-\frac {2}{45} \int \frac {-480-\frac {813 x}{2}+396 x^2}{\left (2+4 x-3 x^2\right ) \left (1+3 x+2 x^2\right )^{3/2}} \, dx\\ &=\frac {2 (21+22 x)}{15 \left (1+3 x+2 x^2\right )^{3/2}}+\frac {2 (273+230 x)}{15 \sqrt {1+3 x+2 x^2}}+\frac {4}{675} \int \frac {\frac {23355}{2}-\frac {27135 x}{4}}{\left (2+4 x-3 x^2\right ) \sqrt {1+3 x+2 x^2}} \, dx\\ &=\frac {2 (21+22 x)}{15 \left (1+3 x+2 x^2\right )^{3/2}}+\frac {2 (273+230 x)}{15 \sqrt {1+3 x+2 x^2}}-\frac {1}{25} \left (3 \left (335-106 \sqrt {10}\right )\right ) \int \frac {1}{\left (4+2 \sqrt {10}-6 x\right ) \sqrt {1+3 x+2 x^2}} \, dx-\frac {1}{25} \left (3 \left (335+106 \sqrt {10}\right )\right ) \int \frac {1}{\left (4-2 \sqrt {10}-6 x\right ) \sqrt {1+3 x+2 x^2}} \, dx\\ &=\frac {2 (21+22 x)}{15 \left (1+3 x+2 x^2\right )^{3/2}}+\frac {2 (273+230 x)}{15 \sqrt {1+3 x+2 x^2}}+\frac {1}{25} \left (6 \left (335-106 \sqrt {10}\right )\right ) \text {Subst}\left (\int \frac {1}{144+72 \left (4+2 \sqrt {10}\right )+8 \left (4+2 \sqrt {10}\right )^2-x^2} \, dx,x,\frac {-12-3 \left (4+2 \sqrt {10}\right )-\left (18+4 \left (4+2 \sqrt {10}\right )\right ) x}{\sqrt {1+3 x+2 x^2}}\right )+\frac {1}{25} \left (6 \left (335+106 \sqrt {10}\right )\right ) \text {Subst}\left (\int \frac {1}{144+72 \left (4-2 \sqrt {10}\right )+8 \left (4-2 \sqrt {10}\right )^2-x^2} \, dx,x,\frac {-12-3 \left (4-2 \sqrt {10}\right )-\left (18+4 \left (4-2 \sqrt {10}\right )\right ) x}{\sqrt {1+3 x+2 x^2}}\right )\\ &=\frac {2 (21+22 x)}{15 \left (1+3 x+2 x^2\right )^{3/2}}+\frac {2 (273+230 x)}{15 \sqrt {1+3 x+2 x^2}}-\frac {1}{50} \sqrt {\frac {1}{3} \left (4885115+1544809 \sqrt {10}\right )} \tanh ^{-1}\left (\frac {3 \left (4-\sqrt {10}\right )+\left (17-4 \sqrt {10}\right ) x}{2 \sqrt {55-17 \sqrt {10}} \sqrt {1+3 x+2 x^2}}\right )+\frac {1}{50} \sqrt {\frac {1}{3} \left (4885115-1544809 \sqrt {10}\right )} \tanh ^{-1}\left (\frac {3 \left (4+\sqrt {10}\right )+\left (17+4 \sqrt {10}\right ) x}{2 \sqrt {55+17 \sqrt {10}} \sqrt {1+3 x+2 x^2}}\right )\\ \end {align*}
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Mathematica [A]
time = 0.89, size = 154, normalized size = 0.78 \begin {gather*} \frac {2 \sqrt {1+3 x+2 x^2} \left (294+1071 x+1236 x^2+460 x^3\right )}{15 (1+x)^2 (1+2 x)^2}-\frac {1}{75} \sqrt {14655345+4634427 \sqrt {10}} \tanh ^{-1}\left (\frac {\sqrt {1-\sqrt {\frac {2}{5}}} \sqrt {1+3 x+2 x^2}}{1+2 x}\right )+\frac {81 \tanh ^{-1}\left (\frac {\sqrt {1+\sqrt {\frac {2}{5}}} \sqrt {1+3 x+2 x^2}}{1+2 x}\right )}{5 \sqrt {24425575+7724045 \sqrt {10}}} \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. \(877\) vs.
\(2(141)=282\).
time = 0.60, size = 878, normalized size = 4.46
method | result | size |
trager | \(\frac {\frac {184}{3} x^{3}+\frac {824}{5} x^{2}+\frac {714}{5} x +\frac {196}{5}}{\left (2 x^{2}+3 x +1\right )^{\frac {3}{2}}}+\frac {2 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right ) \ln \left (-\frac {22695840000 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{5} x +540905633498400 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{3} x +1201243478400 \sqrt {2 x^{2}+3 x +1}\, \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2}+525911068418400 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{3}-5908432074489101275 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right ) x -12042322347390237 \sqrt {2 x^{2}+3 x +1}-4281865136972328150 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )}{1200 x \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2}-1795497 x +3089618}\right )}{5}+\frac {\RootOf \left (\textit {\_Z}^{2}+3600 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2}-29310690\right ) \ln \left (\frac {-504352000 \RootOf \left (\textit {\_Z}^{2}+3600 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2}-29310690\right ) \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{4} x +20232850257120 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2} \RootOf \left (\textit {\_Z}^{2}+3600 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2}-29310690\right ) x +1601657971200 \sqrt {2 x^{2}+3 x +1}\, \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2}+11686912631520 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2} \RootOf \left (\textit {\_Z}^{2}+3600 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2}-29310690\right )-1087910594433 \RootOf \left (\textit {\_Z}^{2}+3600 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2}-29310690\right ) x +3015957496555836 \sqrt {2 x^{2}+3 x +1}-628400494638 \RootOf \left (\textit {\_Z}^{2}+3600 \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2}-29310690\right )}{1200 x \RootOf \left (96000 \textit {\_Z}^{4}-781618400 \textit {\_Z}^{2}+6561\right )^{2}-7974733 x -3089618}\right )}{150}\) | \(471\) |
default | \(\text {Expression too large to display}\) | \(878\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1276 vs.
\(2 (141) = 282\).
time = 0.54, size = 1276, normalized size = 6.48 \begin {gather*} -\frac {1}{300} \, \sqrt {10} {\left (\frac {980 \, \sqrt {10} x}{17 \, \sqrt {10} {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}} + 55 \, {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}}} - \frac {980 \, \sqrt {10} x}{17 \, \sqrt {10} {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}} - 55 \, {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}}} + \frac {5292 \, \sqrt {10} x}{374 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} + 1183 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} - \frac {5292 \, \sqrt {10} x}{374 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} - 1183 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} - \frac {15680 \, \sqrt {10} x}{17 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} + 55 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} + \frac {15680 \, \sqrt {10} x}{17 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} - 55 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} + \frac {3520 \, x}{17 \, \sqrt {10} {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}} + 55 \, {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}}} + \frac {3520 \, x}{17 \, \sqrt {10} {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}} - 55 \, {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}}} + \frac {19008 \, x}{374 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} + 1183 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} + \frac {19008 \, x}{374 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} - 1183 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} - \frac {56320 \, x}{17 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} + 55 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} - \frac {56320 \, x}{17 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} - 55 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} + \frac {750 \, \sqrt {10}}{17 \, \sqrt {10} {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}} + 55 \, {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}}} - \frac {750 \, \sqrt {10}}{17 \, \sqrt {10} {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}} - 55 \, {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}}} + \frac {4050 \, \sqrt {10}}{374 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} + 1183 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} - \frac {4050 \, \sqrt {10}}{374 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} - 1183 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} - \frac {11760 \, \sqrt {10}}{17 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} + 55 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} + \frac {11760 \, \sqrt {10}}{17 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} - 55 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} + \frac {2760}{17 \, \sqrt {10} {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}} + 55 \, {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}}} + \frac {2760}{17 \, \sqrt {10} {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}} - 55 \, {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}}} + \frac {14904}{374 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} + 1183 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} + \frac {14904}{374 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} - 1183 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} - \frac {42240}{17 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} + 55 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} - \frac {42240}{17 \, \sqrt {10} \sqrt {2 \, x^{2} + 3 \, x + 1} - 55 \, \sqrt {2 \, x^{2} + 3 \, x + 1}} - \frac {1215 \, \sqrt {10} \log \left (\frac {2}{9} \, \sqrt {10} + \frac {2 \, \sqrt {2 \, x^{2} + 3 \, x + 1} \sqrt {17 \, \sqrt {10} + 55}}{3 \, {\left | 6 \, x - 2 \, \sqrt {10} - 4 \right |}} + \frac {34 \, \sqrt {10}}{9 \, {\left | 6 \, x - 2 \, \sqrt {10} - 4 \right |}} + \frac {110}{9 \, {\left | 6 \, x - 2 \, \sqrt {10} - 4 \right |}} + \frac {17}{18}\right )}{{\left (17 \, \sqrt {10} + 55\right )}^{\frac {5}{2}}} - \frac {5 \, \sqrt {10} \log \left (-\frac {2}{9} \, \sqrt {10} + \frac {2 \, \sqrt {2 \, x^{2} + 3 \, x + 1} \sqrt {-\frac {17}{9} \, \sqrt {10} + \frac {55}{9}}}{{\left | 6 \, x + 2 \, \sqrt {10} - 4 \right |}} - \frac {34 \, \sqrt {10}}{9 \, {\left | 6 \, x + 2 \, \sqrt {10} - 4 \right |}} + \frac {110}{9 \, {\left | 6 \, x + 2 \, \sqrt {10} - 4 \right |}} + \frac {17}{18}\right )}{{\left (-\frac {17}{9} \, \sqrt {10} + \frac {55}{9}\right )}^{\frac {5}{2}}} - \frac {9720 \, \log \left (\frac {2}{9} \, \sqrt {10} + \frac {2 \, \sqrt {2 \, x^{2} + 3 \, x + 1} \sqrt {17 \, \sqrt {10} + 55}}{3 \, {\left | 6 \, x - 2 \, \sqrt {10} - 4 \right |}} + \frac {34 \, \sqrt {10}}{9 \, {\left | 6 \, x - 2 \, \sqrt {10} - 4 \right |}} + \frac {110}{9 \, {\left | 6 \, x - 2 \, \sqrt {10} - 4 \right |}} + \frac {17}{18}\right )}{{\left (17 \, \sqrt {10} + 55\right )}^{\frac {5}{2}}} + \frac {40 \, \log \left (-\frac {2}{9} \, \sqrt {10} + \frac {2 \, \sqrt {2 \, x^{2} + 3 \, x + 1} \sqrt {-\frac {17}{9} \, \sqrt {10} + \frac {55}{9}}}{{\left | 6 \, x + 2 \, \sqrt {10} - 4 \right |}} - \frac {34 \, \sqrt {10}}{9 \, {\left | 6 \, x + 2 \, \sqrt {10} - 4 \right |}} + \frac {110}{9 \, {\left | 6 \, x + 2 \, \sqrt {10} - 4 \right |}} + \frac {17}{18}\right )}{{\left (-\frac {17}{9} \, \sqrt {10} + \frac {55}{9}\right )}^{\frac {5}{2}}}\right )} \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. 435 vs.
\(2 (141) = 282\).
time = 0.42, size = 435, normalized size = 2.21 \begin {gather*} \frac {23520 \, x^{4} + 70560 \, x^{3} + \sqrt {3} {\left (4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 6 \, x + 1\right )} \sqrt {1544809 \, \sqrt {10} + 4885115} \log \left (-\frac {243 \, \sqrt {10} x + {\left (893 \, \sqrt {10} \sqrt {3} x - 2824 \, \sqrt {3} x\right )} \sqrt {1544809 \, \sqrt {10} + 4885115} + 486 \, x - 486 \, \sqrt {2 \, x^{2} + 3 \, x + 1} + 486}{x}\right ) - \sqrt {3} {\left (4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 6 \, x + 1\right )} \sqrt {1544809 \, \sqrt {10} + 4885115} \log \left (-\frac {243 \, \sqrt {10} x - {\left (893 \, \sqrt {10} \sqrt {3} x - 2824 \, \sqrt {3} x\right )} \sqrt {1544809 \, \sqrt {10} + 4885115} + 486 \, x - 486 \, \sqrt {2 \, x^{2} + 3 \, x + 1} + 486}{x}\right ) + \sqrt {3} {\left (4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 6 \, x + 1\right )} \sqrt {-1544809 \, \sqrt {10} + 4885115} \log \left (\frac {243 \, \sqrt {10} x + {\left (893 \, \sqrt {10} \sqrt {3} x + 2824 \, \sqrt {3} x\right )} \sqrt {-1544809 \, \sqrt {10} + 4885115} - 486 \, x + 486 \, \sqrt {2 \, x^{2} + 3 \, x + 1} - 486}{x}\right ) - \sqrt {3} {\left (4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 6 \, x + 1\right )} \sqrt {-1544809 \, \sqrt {10} + 4885115} \log \left (\frac {243 \, \sqrt {10} x - {\left (893 \, \sqrt {10} \sqrt {3} x + 2824 \, \sqrt {3} x\right )} \sqrt {-1544809 \, \sqrt {10} + 4885115} - 486 \, x + 486 \, \sqrt {2 \, x^{2} + 3 \, x + 1} - 486}{x}\right ) + 76440 \, x^{2} + 20 \, {\left (460 \, x^{3} + 1236 \, x^{2} + 1071 \, x + 294\right )} \sqrt {2 \, x^{2} + 3 \, x + 1} + 35280 \, x + 5880}{150 \, {\left (4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 6 \, x + 1\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 {x}{12 x^{6} \sqrt {2 x^{2} + 3 x + 1} + 20 x^{5} \sqrt {2 x^{2} + 3 x + 1} - 17 x^{4} \sqrt {2 x^{2} + 3 x + 1} - 58 x^{3} \sqrt {2 x^{2} + 3 x + 1} - 47 x^{2} \sqrt {2 x^{2} + 3 x + 1} - 16 x \sqrt {2 x^{2} + 3 x + 1} - 2 \sqrt {2 x^{2} + 3 x + 1}}\, dx - \int \frac {2}{12 x^{6} \sqrt {2 x^{2} + 3 x + 1} + 20 x^{5} \sqrt {2 x^{2} + 3 x + 1} - 17 x^{4} \sqrt {2 x^{2} + 3 x + 1} - 58 x^{3} \sqrt {2 x^{2} + 3 x + 1} - 47 x^{2} \sqrt {2 x^{2} + 3 x + 1} - 16 x \sqrt {2 x^{2} + 3 x + 1} - 2 \sqrt {2 x^{2} + 3 x + 1}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.77, size = 121, normalized size = 0.61 \begin {gather*} \frac {2 \, {\left ({\left (4 \, {\left (115 \, x + 309\right )} x + 1071\right )} x + 294\right )}}{15 \, {\left (2 \, x^{2} + 3 \, x + 1\right )}^{\frac {3}{2}}} + 0.00115890443050800 \, \log \left (-\sqrt {2} x + \sqrt {2 \, x^{2} + 3 \, x + 1} + 5.90976932712000\right ) - 36.0928986365333 \, \log \left (-\sqrt {2} x + \sqrt {2 \, x^{2} + 3 \, x + 1} - 0.176527156327000\right ) + 36.0928986365333 \, \log \left (-\sqrt {2} x + \sqrt {2 \, x^{2} + 3 \, x + 1} - 0.919278730509000\right ) - 0.00115890442528267 \, \log \left (-\sqrt {2} x + \sqrt {2 \, x^{2} + 3 \, x + 1} - 1.04272727395000\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int \frac {x+2}{{\left (2\,x^2+3\,x+1\right )}^{5/2}\,\left (-3\,x^2+4\,x+2\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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