Optimal. Leaf size=385 \[ -\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (\frac {1}{a x}+1\right )^{9/4}-\frac {2 a^3 \left (\frac {1}{a x}+1\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {11}{4} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (\frac {1}{a x}+1\right )^{5/4}-\frac {55}{8} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \sqrt [4]{\frac {1}{a x}+1}-\frac {55 a^3 \log \left (\frac {\sqrt {1-\frac {1}{a x}}}{\sqrt {\frac {1}{a x}+1}}-\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{\frac {1}{a x}+1}}+1\right )}{16 \sqrt {2}}+\frac {55 a^3 \log \left (\frac {\sqrt {1-\frac {1}{a x}}}{\sqrt {\frac {1}{a x}+1}}+\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{\frac {1}{a x}+1}}+1\right )}{16 \sqrt {2}}+\frac {55 a^3 \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{\frac {1}{a x}+1}}\right )}{8 \sqrt {2}}-\frac {55 a^3 \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{\frac {1}{a x}+1}}+1\right )}{8 \sqrt {2}} \]
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Rubi [A] time = 0.31, antiderivative size = 385, normalized size of antiderivative = 1.00, number of steps used = 16, number of rules used = 12, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.857, Rules used = {6171, 89, 80, 50, 63, 331, 297, 1162, 617, 204, 1165, 628} \[ -\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (\frac {1}{a x}+1\right )^{9/4}-\frac {2 a^3 \left (\frac {1}{a x}+1\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {11}{4} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (\frac {1}{a x}+1\right )^{5/4}-\frac {55}{8} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \sqrt [4]{\frac {1}{a x}+1}-\frac {55 a^3 \log \left (\frac {\sqrt {1-\frac {1}{a x}}}{\sqrt {\frac {1}{a x}+1}}-\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{\frac {1}{a x}+1}}+1\right )}{16 \sqrt {2}}+\frac {55 a^3 \log \left (\frac {\sqrt {1-\frac {1}{a x}}}{\sqrt {\frac {1}{a x}+1}}+\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{\frac {1}{a x}+1}}+1\right )}{16 \sqrt {2}}+\frac {55 a^3 \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{\frac {1}{a x}+1}}\right )}{8 \sqrt {2}}-\frac {55 a^3 \tan ^{-1}\left (\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{\frac {1}{a x}+1}}+1\right )}{8 \sqrt {2}} \]
Antiderivative was successfully verified.
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Rule 50
Rule 63
Rule 80
Rule 89
Rule 204
Rule 297
Rule 331
Rule 617
Rule 628
Rule 1162
Rule 1165
Rule 6171
Rubi steps
\begin {align*} \int \frac {e^{\frac {5}{2} \coth ^{-1}(a x)}}{x^4} \, dx &=-\operatorname {Subst}\left (\int \frac {x^2 \left (1+\frac {x}{a}\right )^{5/4}}{\left (1-\frac {x}{a}\right )^{5/4}} \, dx,x,\frac {1}{x}\right )\\ &=-\frac {2 a^3 \left (1+\frac {1}{a x}\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}+\left (2 a^3\right ) \operatorname {Subst}\left (\int \frac {\left (\frac {5}{2 a}+\frac {x}{2 a^2}\right ) \left (1+\frac {x}{a}\right )^{5/4}}{\sqrt [4]{1-\frac {x}{a}}} \, dx,x,\frac {1}{x}\right )\\ &=-\frac {2 a^3 \left (1+\frac {1}{a x}\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{9/4}+\frac {1}{2} \left (11 a^2\right ) \operatorname {Subst}\left (\int \frac {\left (1+\frac {x}{a}\right )^{5/4}}{\sqrt [4]{1-\frac {x}{a}}} \, dx,x,\frac {1}{x}\right )\\ &=-\frac {11}{4} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{5/4}-\frac {2 a^3 \left (1+\frac {1}{a x}\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{9/4}+\frac {1}{8} \left (55 a^2\right ) \operatorname {Subst}\left (\int \frac {\sqrt [4]{1+\frac {x}{a}}}{\sqrt [4]{1-\frac {x}{a}}} \, dx,x,\frac {1}{x}\right )\\ &=-\frac {55}{8} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \sqrt [4]{1+\frac {1}{a x}}-\frac {11}{4} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{5/4}-\frac {2 a^3 \left (1+\frac {1}{a x}\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{9/4}+\frac {1}{16} \left (55 a^2\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt [4]{1-\frac {x}{a}} \left (1+\frac {x}{a}\right )^{3/4}} \, dx,x,\frac {1}{x}\right )\\ &=-\frac {55}{8} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \sqrt [4]{1+\frac {1}{a x}}-\frac {11}{4} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{5/4}-\frac {2 a^3 \left (1+\frac {1}{a x}\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{9/4}-\frac {1}{4} \left (55 a^3\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (2-x^4\right )^{3/4}} \, dx,x,\sqrt [4]{1-\frac {1}{a x}}\right )\\ &=-\frac {55}{8} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \sqrt [4]{1+\frac {1}{a x}}-\frac {11}{4} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{5/4}-\frac {2 a^3 \left (1+\frac {1}{a x}\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{9/4}-\frac {1}{4} \left (55 a^3\right ) \operatorname {Subst}\left (\int \frac {x^2}{1+x^4} \, dx,x,\frac {\sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )\\ &=-\frac {55}{8} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \sqrt [4]{1+\frac {1}{a x}}-\frac {11}{4} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{5/4}-\frac {2 a^3 \left (1+\frac {1}{a x}\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{9/4}+\frac {1}{8} \left (55 a^3\right ) \operatorname {Subst}\left (\int \frac {1-x^2}{1+x^4} \, dx,x,\frac {\sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )-\frac {1}{8} \left (55 a^3\right ) \operatorname {Subst}\left (\int \frac {1+x^2}{1+x^4} \, dx,x,\frac {\sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )\\ &=-\frac {55}{8} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \sqrt [4]{1+\frac {1}{a x}}-\frac {11}{4} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{5/4}-\frac {2 a^3 \left (1+\frac {1}{a x}\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{9/4}-\frac {1}{16} \left (55 a^3\right ) \operatorname {Subst}\left (\int \frac {1}{1-\sqrt {2} x+x^2} \, dx,x,\frac {\sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )-\frac {1}{16} \left (55 a^3\right ) \operatorname {Subst}\left (\int \frac {1}{1+\sqrt {2} x+x^2} \, dx,x,\frac {\sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )-\frac {\left (55 a^3\right ) \operatorname {Subst}\left (\int \frac {\sqrt {2}+2 x}{-1-\sqrt {2} x-x^2} \, dx,x,\frac {\sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )}{16 \sqrt {2}}-\frac {\left (55 a^3\right ) \operatorname {Subst}\left (\int \frac {\sqrt {2}-2 x}{-1+\sqrt {2} x-x^2} \, dx,x,\frac {\sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )}{16 \sqrt {2}}\\ &=-\frac {55}{8} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \sqrt [4]{1+\frac {1}{a x}}-\frac {11}{4} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{5/4}-\frac {2 a^3 \left (1+\frac {1}{a x}\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{9/4}-\frac {55 a^3 \log \left (1+\frac {\sqrt {1-\frac {1}{a x}}}{\sqrt {1+\frac {1}{a x}}}-\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )}{16 \sqrt {2}}+\frac {55 a^3 \log \left (1+\frac {\sqrt {1-\frac {1}{a x}}}{\sqrt {1+\frac {1}{a x}}}+\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )}{16 \sqrt {2}}-\frac {\left (55 a^3\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1-\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )}{8 \sqrt {2}}+\frac {\left (55 a^3\right ) \operatorname {Subst}\left (\int \frac {1}{-1-x^2} \, dx,x,1+\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )}{8 \sqrt {2}}\\ &=-\frac {55}{8} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \sqrt [4]{1+\frac {1}{a x}}-\frac {11}{4} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{5/4}-\frac {2 a^3 \left (1+\frac {1}{a x}\right )^{9/4}}{\sqrt [4]{1-\frac {1}{a x}}}-\frac {1}{3} a^3 \left (1-\frac {1}{a x}\right )^{3/4} \left (1+\frac {1}{a x}\right )^{9/4}+\frac {55 a^3 \tan ^{-1}\left (1-\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )}{8 \sqrt {2}}-\frac {55 a^3 \tan ^{-1}\left (1+\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )}{8 \sqrt {2}}-\frac {55 a^3 \log \left (1+\frac {\sqrt {1-\frac {1}{a x}}}{\sqrt {1+\frac {1}{a x}}}-\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )}{16 \sqrt {2}}+\frac {55 a^3 \log \left (1+\frac {\sqrt {1-\frac {1}{a x}}}{\sqrt {1+\frac {1}{a x}}}+\frac {\sqrt {2} \sqrt [4]{1-\frac {1}{a x}}}{\sqrt [4]{1+\frac {1}{a x}}}\right )}{16 \sqrt {2}}\\ \end {align*}
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Mathematica [C] time = 0.15, size = 104, normalized size = 0.27 \[ a^3 \left (-\frac {55}{32} \text {RootSum}\left [\text {$\#$1}^4+1\& ,\frac {\coth ^{-1}(a x)-2 \log \left (e^{\frac {1}{2} \coth ^{-1}(a x)}-\text {$\#$1}\right )}{\text {$\#$1}^3}\& \right ]-\frac {e^{\frac {1}{2} \coth ^{-1}(a x)} \left (462 e^{2 \coth ^{-1}(a x)}+425 e^{4 \coth ^{-1}(a x)}+96 e^{6 \coth ^{-1}(a x)}+165\right )}{12 \left (e^{2 \coth ^{-1}(a x)}+1\right )^3}\right ) \]
Warning: Unable to verify antiderivative.
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fricas [A] time = 0.60, size = 477, normalized size = 1.24 \[ \frac {660 \, \sqrt {2} {\left (a^{12}\right )}^{\frac {1}{4}} {\left (a x^{4} - x^{3}\right )} \arctan \left (-\frac {a^{12} + \sqrt {2} {\left (a^{12}\right )}^{\frac {1}{4}} a^{9} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}} - \sqrt {2} \sqrt {a^{18} \sqrt {\frac {a x - 1}{a x + 1}} + \sqrt {a^{12}} a^{12} + \sqrt {2} {\left (a^{12}\right )}^{\frac {3}{4}} a^{9} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}}} {\left (a^{12}\right )}^{\frac {1}{4}}}{a^{12}}\right ) + 660 \, \sqrt {2} {\left (a^{12}\right )}^{\frac {1}{4}} {\left (a x^{4} - x^{3}\right )} \arctan \left (\frac {a^{12} - \sqrt {2} {\left (a^{12}\right )}^{\frac {1}{4}} a^{9} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}} + \sqrt {2} \sqrt {a^{18} \sqrt {\frac {a x - 1}{a x + 1}} + \sqrt {a^{12}} a^{12} - \sqrt {2} {\left (a^{12}\right )}^{\frac {3}{4}} a^{9} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}}} {\left (a^{12}\right )}^{\frac {1}{4}}}{a^{12}}\right ) + 165 \, \sqrt {2} {\left (a^{12}\right )}^{\frac {1}{4}} {\left (a x^{4} - x^{3}\right )} \log \left (27680640625 \, a^{18} \sqrt {\frac {a x - 1}{a x + 1}} + 27680640625 \, \sqrt {a^{12}} a^{12} + 27680640625 \, \sqrt {2} {\left (a^{12}\right )}^{\frac {3}{4}} a^{9} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}}\right ) - 165 \, \sqrt {2} {\left (a^{12}\right )}^{\frac {1}{4}} {\left (a x^{4} - x^{3}\right )} \log \left (27680640625 \, a^{18} \sqrt {\frac {a x - 1}{a x + 1}} + 27680640625 \, \sqrt {a^{12}} a^{12} - 27680640625 \, \sqrt {2} {\left (a^{12}\right )}^{\frac {3}{4}} a^{9} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}}\right ) - 4 \, {\left (287 \, a^{4} x^{4} + 226 \, a^{3} x^{3} - 87 \, a^{2} x^{2} - 34 \, a x - 8\right )} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {3}{4}}}{96 \, {\left (a x^{4} - x^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 291, normalized size = 0.76 \[ -\frac {1}{96} \, {\left (330 \, \sqrt {2} a^{2} \arctan \left (\frac {1}{2} \, \sqrt {2} {\left (\sqrt {2} + 2 \, \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}}\right )}\right ) + 330 \, \sqrt {2} a^{2} \arctan \left (-\frac {1}{2} \, \sqrt {2} {\left (\sqrt {2} - 2 \, \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}}\right )}\right ) - 165 \, \sqrt {2} a^{2} \log \left (\sqrt {2} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}} + \sqrt {\frac {a x - 1}{a x + 1}} + 1\right ) + 165 \, \sqrt {2} a^{2} \log \left (-\sqrt {2} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}} + \sqrt {\frac {a x - 1}{a x + 1}} + 1\right ) + \frac {768 \, a^{2}}{\left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}}} + \frac {8 \, {\left (\frac {174 \, {\left (a x - 1\right )} a^{2} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {3}{4}}}{a x + 1} + \frac {69 \, {\left (a x - 1\right )}^{2} a^{2} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {3}{4}}}{{\left (a x + 1\right )}^{2}} + 137 \, a^{2} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {3}{4}}\right )}}{{\left (\frac {a x - 1}{a x + 1} + 1\right )}^{3}}\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.37, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (\frac {a x -1}{a x +1}\right )^{\frac {5}{4}} x^{4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 288, normalized size = 0.75 \[ -\frac {1}{96} \, {\left (165 \, {\left (2 \, \sqrt {2} \arctan \left (\frac {1}{2} \, \sqrt {2} {\left (\sqrt {2} + 2 \, \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}}\right )}\right ) + 2 \, \sqrt {2} \arctan \left (-\frac {1}{2} \, \sqrt {2} {\left (\sqrt {2} - 2 \, \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}}\right )}\right ) - \sqrt {2} \log \left (\sqrt {2} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}} + \sqrt {\frac {a x - 1}{a x + 1}} + 1\right ) + \sqrt {2} \log \left (-\sqrt {2} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}} + \sqrt {\frac {a x - 1}{a x + 1}} + 1\right )\right )} a^{2} + \frac {8 \, {\left (\frac {425 \, {\left (a x - 1\right )} a^{2}}{a x + 1} + \frac {462 \, {\left (a x - 1\right )}^{2} a^{2}}{{\left (a x + 1\right )}^{2}} + \frac {165 \, {\left (a x - 1\right )}^{3} a^{2}}{{\left (a x + 1\right )}^{3}} + 96 \, a^{2}\right )}}{\left (\frac {a x - 1}{a x + 1}\right )^{\frac {13}{4}} + 3 \, \left (\frac {a x - 1}{a x + 1}\right )^{\frac {9}{4}} + 3 \, \left (\frac {a x - 1}{a x + 1}\right )^{\frac {5}{4}} + \left (\frac {a x - 1}{a x + 1}\right )^{\frac {1}{4}}}\right )} a \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.26, size = 188, normalized size = 0.49 \[ \frac {55\,{\left (-1\right )}^{1/4}\,a^3\,\mathrm {atanh}\left ({\left (-1\right )}^{1/4}\,{\left (\frac {a\,x-1}{a\,x+1}\right )}^{1/4}\right )}{8}-\frac {55\,{\left (-1\right )}^{1/4}\,a^3\,\mathrm {atan}\left ({\left (-1\right )}^{1/4}\,{\left (\frac {a\,x-1}{a\,x+1}\right )}^{1/4}\right )}{8}-\frac {8\,a^3+\frac {77\,a^3\,{\left (a\,x-1\right )}^2}{2\,{\left (a\,x+1\right )}^2}+\frac {55\,a^3\,{\left (a\,x-1\right )}^3}{4\,{\left (a\,x+1\right )}^3}+\frac {425\,a^3\,\left (a\,x-1\right )}{12\,\left (a\,x+1\right )}}{{\left (\frac {a\,x-1}{a\,x+1}\right )}^{1/4}+3\,{\left (\frac {a\,x-1}{a\,x+1}\right )}^{5/4}+3\,{\left (\frac {a\,x-1}{a\,x+1}\right )}^{9/4}+{\left (\frac {a\,x-1}{a\,x+1}\right )}^{13/4}} \]
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 \[ \int \frac {1}{x^{4} \left (\frac {a x - 1}{a x + 1}\right )^{\frac {5}{4}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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