Optimal. Leaf size=351 \[ -\frac {11 (17 A b-5 a B)}{180 a^3 b x^{5/2}}+\frac {A b-a B}{6 a b x^{5/2} \left (a+b x^3\right )^2}+\frac {17 A b-5 a B}{36 a^2 b x^{5/2} \left (a+b x^3\right )}+\frac {11 (17 A b-5 a B) \tan ^{-1}\left (\sqrt {3}-\frac {2 \sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{216 a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B) \tan ^{-1}\left (\sqrt {3}+\frac {2 \sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{216 a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B) \tan ^{-1}\left (\frac {\sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{108 a^{23/6} \sqrt [6]{b}}+\frac {11 (17 A b-5 a B) \log \left (\sqrt [3]{a}-\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} \sqrt {x}+\sqrt [3]{b} x\right )}{144 \sqrt {3} a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B) \log \left (\sqrt [3]{a}+\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} \sqrt {x}+\sqrt [3]{b} x\right )}{144 \sqrt {3} a^{23/6} \sqrt [6]{b}} \]
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Rubi [A]
time = 0.38, antiderivative size = 351, normalized size of antiderivative = 1.00, number of steps
used = 14, number of rules used = 10, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.454, Rules used = {468, 296,
331, 335, 215, 648, 632, 210, 642, 211} \begin {gather*} \frac {11 (17 A b-5 a B) \text {ArcTan}\left (\sqrt {3}-\frac {2 \sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{216 a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B) \text {ArcTan}\left (\frac {2 \sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}+\sqrt {3}\right )}{216 a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B) \text {ArcTan}\left (\frac {\sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{108 a^{23/6} \sqrt [6]{b}}+\frac {11 (17 A b-5 a B) \log \left (-\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} \sqrt {x}+\sqrt [3]{a}+\sqrt [3]{b} x\right )}{144 \sqrt {3} a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B) \log \left (\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} \sqrt {x}+\sqrt [3]{a}+\sqrt [3]{b} x\right )}{144 \sqrt {3} a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B)}{180 a^3 b x^{5/2}}+\frac {17 A b-5 a B}{36 a^2 b x^{5/2} \left (a+b x^3\right )}+\frac {A b-a B}{6 a b x^{5/2} \left (a+b x^3\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 210
Rule 211
Rule 215
Rule 296
Rule 331
Rule 335
Rule 468
Rule 632
Rule 642
Rule 648
Rubi steps
\begin {align*} \int \frac {A+B x^3}{x^{7/2} \left (a+b x^3\right )^3} \, dx &=\frac {A b-a B}{6 a b x^{5/2} \left (a+b x^3\right )^2}+\frac {\left (\frac {17 A b}{2}-\frac {5 a B}{2}\right ) \int \frac {1}{x^{7/2} \left (a+b x^3\right )^2} \, dx}{6 a b}\\ &=\frac {A b-a B}{6 a b x^{5/2} \left (a+b x^3\right )^2}+\frac {17 A b-5 a B}{36 a^2 b x^{5/2} \left (a+b x^3\right )}+\frac {(11 (17 A b-5 a B)) \int \frac {1}{x^{7/2} \left (a+b x^3\right )} \, dx}{72 a^2 b}\\ &=-\frac {11 (17 A b-5 a B)}{180 a^3 b x^{5/2}}+\frac {A b-a B}{6 a b x^{5/2} \left (a+b x^3\right )^2}+\frac {17 A b-5 a B}{36 a^2 b x^{5/2} \left (a+b x^3\right )}-\frac {(11 (17 A b-5 a B)) \int \frac {1}{\sqrt {x} \left (a+b x^3\right )} \, dx}{72 a^3}\\ &=-\frac {11 (17 A b-5 a B)}{180 a^3 b x^{5/2}}+\frac {A b-a B}{6 a b x^{5/2} \left (a+b x^3\right )^2}+\frac {17 A b-5 a B}{36 a^2 b x^{5/2} \left (a+b x^3\right )}-\frac {(11 (17 A b-5 a B)) \text {Subst}\left (\int \frac {1}{a+b x^6} \, dx,x,\sqrt {x}\right )}{36 a^3}\\ &=-\frac {11 (17 A b-5 a B)}{180 a^3 b x^{5/2}}+\frac {A b-a B}{6 a b x^{5/2} \left (a+b x^3\right )^2}+\frac {17 A b-5 a B}{36 a^2 b x^{5/2} \left (a+b x^3\right )}-\frac {(11 (17 A b-5 a B)) \text {Subst}\left (\int \frac {\sqrt [6]{a}-\frac {1}{2} \sqrt {3} \sqrt [6]{b} x}{\sqrt [3]{a}-\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} x+\sqrt [3]{b} x^2} \, dx,x,\sqrt {x}\right )}{108 a^{23/6}}-\frac {(11 (17 A b-5 a B)) \text {Subst}\left (\int \frac {\sqrt [6]{a}+\frac {1}{2} \sqrt {3} \sqrt [6]{b} x}{\sqrt [3]{a}+\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} x+\sqrt [3]{b} x^2} \, dx,x,\sqrt {x}\right )}{108 a^{23/6}}-\frac {(11 (17 A b-5 a B)) \text {Subst}\left (\int \frac {1}{\sqrt [3]{a}+\sqrt [3]{b} x^2} \, dx,x,\sqrt {x}\right )}{108 a^{11/3}}\\ &=-\frac {11 (17 A b-5 a B)}{180 a^3 b x^{5/2}}+\frac {A b-a B}{6 a b x^{5/2} \left (a+b x^3\right )^2}+\frac {17 A b-5 a B}{36 a^2 b x^{5/2} \left (a+b x^3\right )}-\frac {11 (17 A b-5 a B) \tan ^{-1}\left (\frac {\sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{108 a^{23/6} \sqrt [6]{b}}-\frac {(11 (17 A b-5 a B)) \text {Subst}\left (\int \frac {1}{\sqrt [3]{a}-\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} x+\sqrt [3]{b} x^2} \, dx,x,\sqrt {x}\right )}{432 a^{11/3}}-\frac {(11 (17 A b-5 a B)) \text {Subst}\left (\int \frac {1}{\sqrt [3]{a}+\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} x+\sqrt [3]{b} x^2} \, dx,x,\sqrt {x}\right )}{432 a^{11/3}}+\frac {(11 (17 A b-5 a B)) \text {Subst}\left (\int \frac {-\sqrt {3} \sqrt [6]{a} \sqrt [6]{b}+2 \sqrt [3]{b} x}{\sqrt [3]{a}-\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} x+\sqrt [3]{b} x^2} \, dx,x,\sqrt {x}\right )}{144 \sqrt {3} a^{23/6} \sqrt [6]{b}}-\frac {(11 (17 A b-5 a B)) \text {Subst}\left (\int \frac {\sqrt {3} \sqrt [6]{a} \sqrt [6]{b}+2 \sqrt [3]{b} x}{\sqrt [3]{a}+\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} x+\sqrt [3]{b} x^2} \, dx,x,\sqrt {x}\right )}{144 \sqrt {3} a^{23/6} \sqrt [6]{b}}\\ &=-\frac {11 (17 A b-5 a B)}{180 a^3 b x^{5/2}}+\frac {A b-a B}{6 a b x^{5/2} \left (a+b x^3\right )^2}+\frac {17 A b-5 a B}{36 a^2 b x^{5/2} \left (a+b x^3\right )}-\frac {11 (17 A b-5 a B) \tan ^{-1}\left (\frac {\sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{108 a^{23/6} \sqrt [6]{b}}+\frac {11 (17 A b-5 a B) \log \left (\sqrt [3]{a}-\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} \sqrt {x}+\sqrt [3]{b} x\right )}{144 \sqrt {3} a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B) \log \left (\sqrt [3]{a}+\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} \sqrt {x}+\sqrt [3]{b} x\right )}{144 \sqrt {3} a^{23/6} \sqrt [6]{b}}-\frac {(11 (17 A b-5 a B)) \text {Subst}\left (\int \frac {1}{-\frac {1}{3}-x^2} \, dx,x,1-\frac {2 \sqrt [6]{b} \sqrt {x}}{\sqrt {3} \sqrt [6]{a}}\right )}{216 \sqrt {3} a^{23/6} \sqrt [6]{b}}+\frac {(11 (17 A b-5 a B)) \text {Subst}\left (\int \frac {1}{-\frac {1}{3}-x^2} \, dx,x,1+\frac {2 \sqrt [6]{b} \sqrt {x}}{\sqrt {3} \sqrt [6]{a}}\right )}{216 \sqrt {3} a^{23/6} \sqrt [6]{b}}\\ &=-\frac {11 (17 A b-5 a B)}{180 a^3 b x^{5/2}}+\frac {A b-a B}{6 a b x^{5/2} \left (a+b x^3\right )^2}+\frac {17 A b-5 a B}{36 a^2 b x^{5/2} \left (a+b x^3\right )}+\frac {11 (17 A b-5 a B) \tan ^{-1}\left (\sqrt {3}-\frac {2 \sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{216 a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B) \tan ^{-1}\left (\sqrt {3}+\frac {2 \sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{216 a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B) \tan ^{-1}\left (\frac {\sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{108 a^{23/6} \sqrt [6]{b}}+\frac {11 (17 A b-5 a B) \log \left (\sqrt [3]{a}-\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} \sqrt {x}+\sqrt [3]{b} x\right )}{144 \sqrt {3} a^{23/6} \sqrt [6]{b}}-\frac {11 (17 A b-5 a B) \log \left (\sqrt [3]{a}+\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} \sqrt {x}+\sqrt [3]{b} x\right )}{144 \sqrt {3} a^{23/6} \sqrt [6]{b}}\\ \end {align*}
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Mathematica [A]
time = 0.56, size = 209, normalized size = 0.60 \begin {gather*} \frac {-\frac {6 a^{5/6} \left (187 A b^2 x^6+a^2 \left (72 A-85 B x^3\right )+a b x^3 \left (289 A-55 B x^3\right )\right )}{x^{5/2} \left (a+b x^3\right )^2}+\frac {110 (-17 A b+5 a B) \tan ^{-1}\left (\frac {\sqrt [6]{b} \sqrt {x}}{\sqrt [6]{a}}\right )}{\sqrt [6]{b}}+\frac {55 (17 A b-5 a B) \tan ^{-1}\left (\frac {\sqrt [3]{a}-\sqrt [3]{b} x}{\sqrt [6]{a} \sqrt [6]{b} \sqrt {x}}\right )}{\sqrt [6]{b}}+\frac {55 \sqrt {3} (-17 A b+5 a B) \tanh ^{-1}\left (\frac {\sqrt {3} \sqrt [6]{a} \sqrt [6]{b} \sqrt {x}}{\sqrt [3]{a}+\sqrt [3]{b} x}\right )}{\sqrt [6]{b}}}{1080 a^{23/6}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.37, size = 237, normalized size = 0.68
method | result | size |
derivativedivides | \(-\frac {2 \left (\frac {\left (\frac {23}{72} b^{2} A -\frac {11}{72} a b B \right ) x^{\frac {7}{2}}+\frac {a \left (29 A b -17 B a \right ) \sqrt {x}}{72}}{\left (b \,x^{3}+a \right )^{2}}+\frac {11 \left (17 A b -5 B a \right ) \left (\frac {\left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (\frac {\sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{3 a}-\frac {\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \ln \left (\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \sqrt {x}-x -\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{12 a}+\frac {\left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (-\sqrt {3}+\frac {2 \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{6 a}+\frac {\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \ln \left (x +\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \sqrt {x}+\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{12 a}+\frac {\left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (\frac {2 \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}+\sqrt {3}\right )}{6 a}\right )}{72}\right )}{a^{3}}-\frac {2 A}{5 a^{3} x^{\frac {5}{2}}}\) | \(237\) |
default | \(-\frac {2 \left (\frac {\left (\frac {23}{72} b^{2} A -\frac {11}{72} a b B \right ) x^{\frac {7}{2}}+\frac {a \left (29 A b -17 B a \right ) \sqrt {x}}{72}}{\left (b \,x^{3}+a \right )^{2}}+\frac {11 \left (17 A b -5 B a \right ) \left (\frac {\left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (\frac {\sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{3 a}-\frac {\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \ln \left (\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \sqrt {x}-x -\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{12 a}+\frac {\left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (-\sqrt {3}+\frac {2 \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{6 a}+\frac {\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \ln \left (x +\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \sqrt {x}+\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{12 a}+\frac {\left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (\frac {2 \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}+\sqrt {3}\right )}{6 a}\right )}{72}\right )}{a^{3}}-\frac {2 A}{5 a^{3} x^{\frac {5}{2}}}\) | \(237\) |
risch | \(-\frac {2 A}{5 a^{3} x^{\frac {5}{2}}}-\frac {23 x^{\frac {7}{2}} b^{2} A}{36 a^{3} \left (b \,x^{3}+a \right )^{2}}+\frac {11 x^{\frac {7}{2}} b B}{36 a^{2} \left (b \,x^{3}+a \right )^{2}}-\frac {29 A \sqrt {x}\, b}{36 a^{2} \left (b \,x^{3}+a \right )^{2}}+\frac {17 B \sqrt {x}}{36 a \left (b \,x^{3}+a \right )^{2}}-\frac {187 A b \sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \ln \left (x +\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \sqrt {x}+\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{432 a^{4}}-\frac {187 A b \left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (\frac {2 \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}+\sqrt {3}\right )}{216 a^{4}}+\frac {187 A b \sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \ln \left (\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \sqrt {x}-x -\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{432 a^{4}}-\frac {187 A b \left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (-\sqrt {3}+\frac {2 \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{216 a^{4}}-\frac {187 A b \left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (\frac {\sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{108 a^{4}}+\frac {55 B \sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \ln \left (x +\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \sqrt {x}+\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{432 a^{3}}+\frac {55 B \left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (\frac {2 \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}+\sqrt {3}\right )}{216 a^{3}}-\frac {55 B \sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \ln \left (\sqrt {3}\, \left (\frac {a}{b}\right )^{\frac {1}{6}} \sqrt {x}-x -\left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{432 a^{3}}+\frac {55 B \left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (-\sqrt {3}+\frac {2 \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{216 a^{3}}+\frac {55 B \left (\frac {a}{b}\right )^{\frac {1}{6}} \arctan \left (\frac {\sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{108 a^{3}}\) | \(435\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 346, normalized size = 0.99 \begin {gather*} \frac {11 \, {\left (5 \, B a b - 17 \, A b^{2}\right )} x^{6} + 17 \, {\left (5 \, B a^{2} - 17 \, A a b\right )} x^{3} - 72 \, A a^{2}}{180 \, {\left (a^{3} b^{2} x^{\frac {17}{2}} + 2 \, a^{4} b x^{\frac {11}{2}} + a^{5} x^{\frac {5}{2}}\right )}} + \frac {11 \, {\left (\frac {\sqrt {3} {\left (5 \, B a - 17 \, A b\right )} \log \left (\sqrt {3} a^{\frac {1}{6}} b^{\frac {1}{6}} \sqrt {x} + b^{\frac {1}{3}} x + a^{\frac {1}{3}}\right )}{a^{\frac {5}{6}} b^{\frac {1}{6}}} - \frac {\sqrt {3} {\left (5 \, B a - 17 \, A b\right )} \log \left (-\sqrt {3} a^{\frac {1}{6}} b^{\frac {1}{6}} \sqrt {x} + b^{\frac {1}{3}} x + a^{\frac {1}{3}}\right )}{a^{\frac {5}{6}} b^{\frac {1}{6}}} + \frac {4 \, {\left (5 \, B a b^{\frac {1}{3}} - 17 \, A b^{\frac {4}{3}}\right )} \arctan \left (\frac {b^{\frac {1}{3}} \sqrt {x}}{\sqrt {a^{\frac {1}{3}} b^{\frac {1}{3}}}}\right )}{a^{\frac {2}{3}} b^{\frac {1}{3}} \sqrt {a^{\frac {1}{3}} b^{\frac {1}{3}}}} + \frac {2 \, {\left (5 \, B a^{\frac {4}{3}} b^{\frac {1}{3}} - 17 \, A a^{\frac {1}{3}} b^{\frac {4}{3}}\right )} \arctan \left (\frac {\sqrt {3} a^{\frac {1}{6}} b^{\frac {1}{6}} + 2 \, b^{\frac {1}{3}} \sqrt {x}}{\sqrt {a^{\frac {1}{3}} b^{\frac {1}{3}}}}\right )}{a b^{\frac {1}{3}} \sqrt {a^{\frac {1}{3}} b^{\frac {1}{3}}}} + \frac {2 \, {\left (5 \, B a^{\frac {4}{3}} b^{\frac {1}{3}} - 17 \, A a^{\frac {1}{3}} b^{\frac {4}{3}}\right )} \arctan \left (-\frac {\sqrt {3} a^{\frac {1}{6}} b^{\frac {1}{6}} - 2 \, b^{\frac {1}{3}} \sqrt {x}}{\sqrt {a^{\frac {1}{3}} b^{\frac {1}{3}}}}\right )}{a b^{\frac {1}{3}} \sqrt {a^{\frac {1}{3}} b^{\frac {1}{3}}}}\right )}}{432 \, a^{3}} \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. 2690 vs.
\(2 (261) = 522\).
time = 3.32, size = 2690, normalized size = 7.66 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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.
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Giac [A]
time = 1.21, size = 334, normalized size = 0.95 \begin {gather*} \frac {11 \, \sqrt {3} {\left (5 \, \left (a b^{5}\right )^{\frac {1}{6}} B a - 17 \, \left (a b^{5}\right )^{\frac {1}{6}} A b\right )} \log \left (\sqrt {3} \sqrt {x} \left (\frac {a}{b}\right )^{\frac {1}{6}} + x + \left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{432 \, a^{4} b} - \frac {11 \, \sqrt {3} {\left (5 \, \left (a b^{5}\right )^{\frac {1}{6}} B a - 17 \, \left (a b^{5}\right )^{\frac {1}{6}} A b\right )} \log \left (-\sqrt {3} \sqrt {x} \left (\frac {a}{b}\right )^{\frac {1}{6}} + x + \left (\frac {a}{b}\right )^{\frac {1}{3}}\right )}{432 \, a^{4} b} + \frac {11 \, {\left (5 \, \left (a b^{5}\right )^{\frac {1}{6}} B a - 17 \, \left (a b^{5}\right )^{\frac {1}{6}} A b\right )} \arctan \left (\frac {\sqrt {3} \left (\frac {a}{b}\right )^{\frac {1}{6}} + 2 \, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{216 \, a^{4} b} + \frac {11 \, {\left (5 \, \left (a b^{5}\right )^{\frac {1}{6}} B a - 17 \, \left (a b^{5}\right )^{\frac {1}{6}} A b\right )} \arctan \left (-\frac {\sqrt {3} \left (\frac {a}{b}\right )^{\frac {1}{6}} - 2 \, \sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{216 \, a^{4} b} + \frac {11 \, {\left (5 \, \left (a b^{5}\right )^{\frac {1}{6}} B a - 17 \, \left (a b^{5}\right )^{\frac {1}{6}} A b\right )} \arctan \left (\frac {\sqrt {x}}{\left (\frac {a}{b}\right )^{\frac {1}{6}}}\right )}{108 \, a^{4} b} + \frac {11 \, B a b x^{\frac {7}{2}} - 23 \, A b^{2} x^{\frac {7}{2}} + 17 \, B a^{2} \sqrt {x} - 29 \, A a b \sqrt {x}}{36 \, {\left (b x^{3} + a\right )}^{2} a^{3}} - \frac {2 \, A}{5 \, a^{3} x^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.96, size = 2500, normalized size = 7.12 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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