Optimal. Leaf size=1243 \[ \frac {\sqrt {b} (5 b c-7 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} \Pi \left (\frac {\left (\sqrt {b} \sqrt {c}+\sqrt {-a} \sqrt {d}\right )^2}{4 \sqrt {-a} \sqrt {b} \sqrt {c} \sqrt {d}};2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right ) \left (\sqrt {b} \sqrt {c}-\sqrt {-a} \sqrt {d}\right )^2}{64 (-a)^{5/2} \sqrt [4]{c} \sqrt [4]{d} (b c-a d) (b c+a d) \sqrt {d x^8+c}}-\frac {b^{3/4} (5 b c-7 a d) \tan ^{-1}\left (\frac {\sqrt {b c-a d} x^2}{\sqrt [4]{-a} \sqrt [4]{b} \sqrt {d x^8+c}}\right )}{32 (-a)^{9/4} (b c-a d)^{3/2}}-\frac {b^{3/4} (5 b c-7 a d) \tan ^{-1}\left (\frac {\sqrt {a d-b c} x^2}{\sqrt [4]{-a} \sqrt [4]{b} \sqrt {d x^8+c}}\right )}{32 (-a)^{9/4} (a d-b c)^{3/2}}-\frac {\sqrt [4]{d} (5 b c-4 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{8 a^2 c^{3/4} (b c-a d) \sqrt {d x^8+c}}+\frac {\sqrt [4]{d} (5 b c-4 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{16 a^2 c^{3/4} (b c-a d) \sqrt {d x^8+c}}+\frac {b \left (\sqrt {c}-\frac {\sqrt {-a} \sqrt {d}}{\sqrt {b}}\right ) \sqrt [4]{d} (5 b c-7 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{32 a^2 \sqrt [4]{c} (b c-a d) (b c+a d) \sqrt {d x^8+c}}+\frac {b \left (\sqrt {c}+\frac {\sqrt {-a} \sqrt {d}}{\sqrt {b}}\right ) \sqrt [4]{d} (5 b c-7 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{32 a^2 \sqrt [4]{c} (b c-a d) (b c+a d) \sqrt {d x^8+c}}-\frac {\sqrt {b} \left (\sqrt {b} \sqrt {c}+\sqrt {-a} \sqrt {d}\right )^2 (5 b c-7 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} \Pi \left (-\frac {\left (\sqrt {b} \sqrt {c}-\sqrt {-a} \sqrt {d}\right )^2}{4 \sqrt {-a} \sqrt {b} \sqrt {c} \sqrt {d}};2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{64 (-a)^{5/2} \sqrt [4]{c} \sqrt [4]{d} (b c-a d) (b c+a d) \sqrt {d x^8+c}}+\frac {\sqrt {d} (5 b c-4 a d) x^2 \sqrt {d x^8+c}}{8 a^2 c (b c-a d) \left (\sqrt {d} x^4+\sqrt {c}\right )}+\frac {b \sqrt {d x^8+c}}{8 a (b c-a d) x^2 \left (b x^8+a\right )}-\frac {(5 b c-4 a d) \sqrt {d x^8+c}}{8 a^2 c (b c-a d) x^2} \]
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Rubi [A] time = 2.38, antiderivative size = 1243, normalized size of antiderivative = 1.00, number of steps used = 15, number of rules used = 10, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.417, Rules used = {465, 472, 583, 584, 305, 220, 1196, 490, 1217, 1707} \[ \frac {\sqrt {b} (5 b c-7 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} \Pi \left (\frac {\left (\sqrt {b} \sqrt {c}+\sqrt {-a} \sqrt {d}\right )^2}{4 \sqrt {-a} \sqrt {b} \sqrt {c} \sqrt {d}};2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right ) \left (\sqrt {b} \sqrt {c}-\sqrt {-a} \sqrt {d}\right )^2}{64 (-a)^{5/2} \sqrt [4]{c} \sqrt [4]{d} (b c-a d) (b c+a d) \sqrt {d x^8+c}}-\frac {b^{3/4} (5 b c-7 a d) \tan ^{-1}\left (\frac {\sqrt {b c-a d} x^2}{\sqrt [4]{-a} \sqrt [4]{b} \sqrt {d x^8+c}}\right )}{32 (-a)^{9/4} (b c-a d)^{3/2}}-\frac {b^{3/4} (5 b c-7 a d) \tan ^{-1}\left (\frac {\sqrt {a d-b c} x^2}{\sqrt [4]{-a} \sqrt [4]{b} \sqrt {d x^8+c}}\right )}{32 (-a)^{9/4} (a d-b c)^{3/2}}-\frac {\sqrt [4]{d} (5 b c-4 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{8 a^2 c^{3/4} (b c-a d) \sqrt {d x^8+c}}+\frac {\sqrt [4]{d} (5 b c-4 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{16 a^2 c^{3/4} (b c-a d) \sqrt {d x^8+c}}+\frac {b \left (\sqrt {c}-\frac {\sqrt {-a} \sqrt {d}}{\sqrt {b}}\right ) \sqrt [4]{d} (5 b c-7 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{32 a^2 \sqrt [4]{c} (b c-a d) (b c+a d) \sqrt {d x^8+c}}+\frac {b \left (\sqrt {c}+\frac {\sqrt {-a} \sqrt {d}}{\sqrt {b}}\right ) \sqrt [4]{d} (5 b c-7 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{32 a^2 \sqrt [4]{c} (b c-a d) (b c+a d) \sqrt {d x^8+c}}-\frac {\sqrt {b} \left (\sqrt {b} \sqrt {c}+\sqrt {-a} \sqrt {d}\right )^2 (5 b c-7 a d) \left (\sqrt {d} x^4+\sqrt {c}\right ) \sqrt {\frac {d x^8+c}{\left (\sqrt {d} x^4+\sqrt {c}\right )^2}} \Pi \left (-\frac {\left (\sqrt {b} \sqrt {c}-\sqrt {-a} \sqrt {d}\right )^2}{4 \sqrt {-a} \sqrt {b} \sqrt {c} \sqrt {d}};2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{64 (-a)^{5/2} \sqrt [4]{c} \sqrt [4]{d} (b c-a d) (b c+a d) \sqrt {d x^8+c}}+\frac {\sqrt {d} (5 b c-4 a d) x^2 \sqrt {d x^8+c}}{8 a^2 c (b c-a d) \left (\sqrt {d} x^4+\sqrt {c}\right )}+\frac {b \sqrt {d x^8+c}}{8 a (b c-a d) x^2 \left (b x^8+a\right )}-\frac {(5 b c-4 a d) \sqrt {d x^8+c}}{8 a^2 c (b c-a d) x^2} \]
Antiderivative was successfully verified.
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Rule 220
Rule 305
Rule 465
Rule 472
Rule 490
Rule 583
Rule 584
Rule 1196
Rule 1217
Rule 1707
Rubi steps
\begin {align*} \int \frac {1}{x^3 \left (a+b x^8\right )^2 \sqrt {c+d x^8}} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {1}{x^2 \left (a+b x^4\right )^2 \sqrt {c+d x^4}} \, dx,x,x^2\right )\\ &=\frac {b \sqrt {c+d x^8}}{8 a (b c-a d) x^2 \left (a+b x^8\right )}-\frac {\operatorname {Subst}\left (\int \frac {-5 b c+4 a d-3 b d x^4}{x^2 \left (a+b x^4\right ) \sqrt {c+d x^4}} \, dx,x,x^2\right )}{8 a (b c-a d)}\\ &=-\frac {(5 b c-4 a d) \sqrt {c+d x^8}}{8 a^2 c (b c-a d) x^2}+\frac {b \sqrt {c+d x^8}}{8 a (b c-a d) x^2 \left (a+b x^8\right )}+\frac {\operatorname {Subst}\left (\int \frac {x^2 \left (-(b c-2 a d) (5 b c-2 a d)+b d (5 b c-4 a d) x^4\right )}{\left (a+b x^4\right ) \sqrt {c+d x^4}} \, dx,x,x^2\right )}{8 a^2 c (b c-a d)}\\ &=-\frac {(5 b c-4 a d) \sqrt {c+d x^8}}{8 a^2 c (b c-a d) x^2}+\frac {b \sqrt {c+d x^8}}{8 a (b c-a d) x^2 \left (a+b x^8\right )}+\frac {\operatorname {Subst}\left (\int \left (\frac {d (5 b c-4 a d) x^2}{\sqrt {c+d x^4}}+\frac {\left (-5 b^2 c^2+7 a b c d\right ) x^2}{\left (a+b x^4\right ) \sqrt {c+d x^4}}\right ) \, dx,x,x^2\right )}{8 a^2 c (b c-a d)}\\ &=-\frac {(5 b c-4 a d) \sqrt {c+d x^8}}{8 a^2 c (b c-a d) x^2}+\frac {b \sqrt {c+d x^8}}{8 a (b c-a d) x^2 \left (a+b x^8\right )}-\frac {(b (5 b c-7 a d)) \operatorname {Subst}\left (\int \frac {x^2}{\left (a+b x^4\right ) \sqrt {c+d x^4}} \, dx,x,x^2\right )}{8 a^2 (b c-a d)}+\frac {(d (5 b c-4 a d)) \operatorname {Subst}\left (\int \frac {x^2}{\sqrt {c+d x^4}} \, dx,x,x^2\right )}{8 a^2 c (b c-a d)}\\ &=-\frac {(5 b c-4 a d) \sqrt {c+d x^8}}{8 a^2 c (b c-a d) x^2}+\frac {b \sqrt {c+d x^8}}{8 a (b c-a d) x^2 \left (a+b x^8\right )}+\frac {\left (\sqrt {b} (5 b c-7 a d)\right ) \operatorname {Subst}\left (\int \frac {1}{\left (\sqrt {-a}-\sqrt {b} x^2\right ) \sqrt {c+d x^4}} \, dx,x,x^2\right )}{16 a^2 (b c-a d)}-\frac {\left (\sqrt {b} (5 b c-7 a d)\right ) \operatorname {Subst}\left (\int \frac {1}{\left (\sqrt {-a}+\sqrt {b} x^2\right ) \sqrt {c+d x^4}} \, dx,x,x^2\right )}{16 a^2 (b c-a d)}+\frac {\left (\sqrt {d} (5 b c-4 a d)\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {c+d x^4}} \, dx,x,x^2\right )}{8 a^2 \sqrt {c} (b c-a d)}-\frac {\left (\sqrt {d} (5 b c-4 a d)\right ) \operatorname {Subst}\left (\int \frac {1-\frac {\sqrt {d} x^2}{\sqrt {c}}}{\sqrt {c+d x^4}} \, dx,x,x^2\right )}{8 a^2 \sqrt {c} (b c-a d)}\\ &=-\frac {(5 b c-4 a d) \sqrt {c+d x^8}}{8 a^2 c (b c-a d) x^2}+\frac {\sqrt {d} (5 b c-4 a d) x^2 \sqrt {c+d x^8}}{8 a^2 c (b c-a d) \left (\sqrt {c}+\sqrt {d} x^4\right )}+\frac {b \sqrt {c+d x^8}}{8 a (b c-a d) x^2 \left (a+b x^8\right )}-\frac {\sqrt [4]{d} (5 b c-4 a d) \left (\sqrt {c}+\sqrt {d} x^4\right ) \sqrt {\frac {c+d x^8}{\left (\sqrt {c}+\sqrt {d} x^4\right )^2}} E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{8 a^2 c^{3/4} (b c-a d) \sqrt {c+d x^8}}+\frac {\sqrt [4]{d} (5 b c-4 a d) \left (\sqrt {c}+\sqrt {d} x^4\right ) \sqrt {\frac {c+d x^8}{\left (\sqrt {c}+\sqrt {d} x^4\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{16 a^2 c^{3/4} (b c-a d) \sqrt {c+d x^8}}+\frac {\left (b \sqrt {c} \left (\sqrt {b} \sqrt {c}-\sqrt {-a} \sqrt {d}\right ) (5 b c-7 a d)\right ) \operatorname {Subst}\left (\int \frac {1+\frac {\sqrt {d} x^2}{\sqrt {c}}}{\left (\sqrt {-a}-\sqrt {b} x^2\right ) \sqrt {c+d x^4}} \, dx,x,x^2\right )}{16 a^2 (b c-a d) (b c+a d)}-\frac {\left (b \sqrt {c} \left (\sqrt {b} \sqrt {c}+\sqrt {-a} \sqrt {d}\right ) (5 b c-7 a d)\right ) \operatorname {Subst}\left (\int \frac {1+\frac {\sqrt {d} x^2}{\sqrt {c}}}{\left (\sqrt {-a}+\sqrt {b} x^2\right ) \sqrt {c+d x^4}} \, dx,x,x^2\right )}{16 a^2 (b c-a d) (b c+a d)}+\frac {\left (\sqrt {b} \left (\sqrt {b} \sqrt {c}-\sqrt {-a} \sqrt {d}\right ) \sqrt {d} (5 b c-7 a d)\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {c+d x^4}} \, dx,x,x^2\right )}{16 a^2 (b c-a d) (b c+a d)}+\frac {\left (\sqrt {b} \left (\sqrt {b} \sqrt {c}+\sqrt {-a} \sqrt {d}\right ) \sqrt {d} (5 b c-7 a d)\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {c+d x^4}} \, dx,x,x^2\right )}{16 a^2 (b c-a d) (b c+a d)}\\ &=-\frac {(5 b c-4 a d) \sqrt {c+d x^8}}{8 a^2 c (b c-a d) x^2}+\frac {\sqrt {d} (5 b c-4 a d) x^2 \sqrt {c+d x^8}}{8 a^2 c (b c-a d) \left (\sqrt {c}+\sqrt {d} x^4\right )}+\frac {b \sqrt {c+d x^8}}{8 a (b c-a d) x^2 \left (a+b x^8\right )}-\frac {b^{3/4} (5 b c-7 a d) \tan ^{-1}\left (\frac {\sqrt {b c-a d} x^2}{\sqrt [4]{-a} \sqrt [4]{b} \sqrt {c+d x^8}}\right )}{32 (-a)^{9/4} (b c-a d)^{3/2}}-\frac {b^{3/4} (5 b c-7 a d) \tan ^{-1}\left (\frac {\sqrt {-b c+a d} x^2}{\sqrt [4]{-a} \sqrt [4]{b} \sqrt {c+d x^8}}\right )}{32 (-a)^{9/4} (-b c+a d)^{3/2}}-\frac {\sqrt [4]{d} (5 b c-4 a d) \left (\sqrt {c}+\sqrt {d} x^4\right ) \sqrt {\frac {c+d x^8}{\left (\sqrt {c}+\sqrt {d} x^4\right )^2}} E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{8 a^2 c^{3/4} (b c-a d) \sqrt {c+d x^8}}+\frac {\sqrt [4]{d} (5 b c-4 a d) \left (\sqrt {c}+\sqrt {d} x^4\right ) \sqrt {\frac {c+d x^8}{\left (\sqrt {c}+\sqrt {d} x^4\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{16 a^2 c^{3/4} (b c-a d) \sqrt {c+d x^8}}+\frac {\sqrt {b} \left (\sqrt {b} \sqrt {c}-\sqrt {-a} \sqrt {d}\right ) \sqrt [4]{d} (5 b c-7 a d) \left (\sqrt {c}+\sqrt {d} x^4\right ) \sqrt {\frac {c+d x^8}{\left (\sqrt {c}+\sqrt {d} x^4\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{32 a^2 \sqrt [4]{c} (b c-a d) (b c+a d) \sqrt {c+d x^8}}+\frac {\sqrt {b} \left (\sqrt {b} \sqrt {c}+\sqrt {-a} \sqrt {d}\right ) \sqrt [4]{d} (5 b c-7 a d) \left (\sqrt {c}+\sqrt {d} x^4\right ) \sqrt {\frac {c+d x^8}{\left (\sqrt {c}+\sqrt {d} x^4\right )^2}} F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{32 a^2 \sqrt [4]{c} (b c-a d) (b c+a d) \sqrt {c+d x^8}}-\frac {\sqrt {b} \left (\sqrt {b} \sqrt {c}+\sqrt {-a} \sqrt {d}\right )^2 (5 b c-7 a d) \left (\sqrt {c}+\sqrt {d} x^4\right ) \sqrt {\frac {c+d x^8}{\left (\sqrt {c}+\sqrt {d} x^4\right )^2}} \Pi \left (-\frac {\left (\sqrt {b} \sqrt {c}-\sqrt {-a} \sqrt {d}\right )^2}{4 \sqrt {-a} \sqrt {b} \sqrt {c} \sqrt {d}};2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{64 (-a)^{5/2} \sqrt [4]{c} \sqrt [4]{d} (b c-a d) (b c+a d) \sqrt {c+d x^8}}+\frac {\sqrt {b} \left (\sqrt {b} \sqrt {c}-\sqrt {-a} \sqrt {d}\right )^2 (5 b c-7 a d) \left (\sqrt {c}+\sqrt {d} x^4\right ) \sqrt {\frac {c+d x^8}{\left (\sqrt {c}+\sqrt {d} x^4\right )^2}} \Pi \left (\frac {\left (\sqrt {b} \sqrt {c}+\sqrt {-a} \sqrt {d}\right )^2}{4 \sqrt {-a} \sqrt {b} \sqrt {c} \sqrt {d}};2 \tan ^{-1}\left (\frac {\sqrt [4]{d} x^2}{\sqrt [4]{c}}\right )|\frac {1}{2}\right )}{64 (-a)^{5/2} \sqrt [4]{c} \sqrt [4]{d} (b c-a d) (b c+a d) \sqrt {c+d x^8}}\\ \end {align*}
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Mathematica [C] time = 0.34, size = 226, normalized size = 0.18 \[ \frac {-7 x^8 \left (a+b x^8\right ) \sqrt {\frac {d x^8}{c}+1} \left (4 a^2 d^2-12 a b c d+5 b^2 c^2\right ) F_1\left (\frac {3}{4};\frac {1}{2},1;\frac {7}{4};-\frac {d x^8}{c},-\frac {b x^8}{a}\right )+21 a \left (c+d x^8\right ) \left (4 a^2 d-4 a b \left (c-d x^8\right )-5 b^2 c x^8\right )+3 b d x^{16} \left (a+b x^8\right ) \sqrt {\frac {d x^8}{c}+1} (5 b c-4 a d) F_1\left (\frac {7}{4};\frac {1}{2},1;\frac {11}{4};-\frac {d x^8}{c},-\frac {b x^8}{a}\right )}{168 a^3 c x^2 \left (a+b x^8\right ) \sqrt {c+d x^8} (b c-a d)} \]
Warning: Unable to verify antiderivative.
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fricas [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b x^{8} + a\right )}^{2} \sqrt {d x^{8} + c} x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.47, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (b \,x^{8}+a \right )^{2} \sqrt {d \,x^{8}+c}\, x^{3}}\, dx \]
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 \[ \int \frac {1}{{\left (b x^{8} + a\right )}^{2} \sqrt {d x^{8} + c} x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int \frac {1}{x^3\,{\left (b\,x^8+a\right )}^2\,\sqrt {d\,x^8+c}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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