Optimal. Leaf size=106 \[ -\frac{b^4 \left (a+b x^3\right )^9}{19305 a^5 x^{27}}+\frac{b^3 \left (a+b x^3\right )^9}{2145 a^4 x^{30}}-\frac{b^2 \left (a+b x^3\right )^9}{429 a^3 x^{33}}+\frac{b \left (a+b x^3\right )^9}{117 a^2 x^{36}}-\frac{\left (a+b x^3\right )^9}{39 a x^{39}} \]
[Out]
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Rubi [A] time = 0.137152, antiderivative size = 106, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{b^4 \left (a+b x^3\right )^9}{19305 a^5 x^{27}}+\frac{b^3 \left (a+b x^3\right )^9}{2145 a^4 x^{30}}-\frac{b^2 \left (a+b x^3\right )^9}{429 a^3 x^{33}}+\frac{b \left (a+b x^3\right )^9}{117 a^2 x^{36}}-\frac{\left (a+b x^3\right )^9}{39 a x^{39}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^8/x^40,x]
[Out]
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Rubi in Sympy [A] time = 23.7686, size = 109, normalized size = 1.03 \[ - \frac{a^{8}}{39 x^{39}} - \frac{2 a^{7} b}{9 x^{36}} - \frac{28 a^{6} b^{2}}{33 x^{33}} - \frac{28 a^{5} b^{3}}{15 x^{30}} - \frac{70 a^{4} b^{4}}{27 x^{27}} - \frac{7 a^{3} b^{5}}{3 x^{24}} - \frac{4 a^{2} b^{6}}{3 x^{21}} - \frac{4 a b^{7}}{9 x^{18}} - \frac{b^{8}}{15 x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**8/x**40,x)
[Out]
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Mathematica [A] time = 0.0121738, size = 108, normalized size = 1.02 \[ -\frac{a^8}{39 x^{39}}-\frac{2 a^7 b}{9 x^{36}}-\frac{28 a^6 b^2}{33 x^{33}}-\frac{28 a^5 b^3}{15 x^{30}}-\frac{70 a^4 b^4}{27 x^{27}}-\frac{7 a^3 b^5}{3 x^{24}}-\frac{4 a^2 b^6}{3 x^{21}}-\frac{4 a b^7}{9 x^{18}}-\frac{b^8}{15 x^{15}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^8/x^40,x]
[Out]
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Maple [A] time = 0.01, size = 91, normalized size = 0.9 \[ -{\frac{{b}^{8}}{15\,{x}^{15}}}-{\frac{28\,{a}^{5}{b}^{3}}{15\,{x}^{30}}}-{\frac{2\,{a}^{7}b}{9\,{x}^{36}}}-{\frac{{a}^{8}}{39\,{x}^{39}}}-{\frac{28\,{a}^{6}{b}^{2}}{33\,{x}^{33}}}-{\frac{4\,a{b}^{7}}{9\,{x}^{18}}}-{\frac{7\,{a}^{3}{b}^{5}}{3\,{x}^{24}}}-{\frac{70\,{a}^{4}{b}^{4}}{27\,{x}^{27}}}-{\frac{4\,{a}^{2}{b}^{6}}{3\,{x}^{21}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^8/x^40,x)
[Out]
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Maxima [A] time = 1.45825, size = 124, normalized size = 1.17 \[ -\frac{1287 \, b^{8} x^{24} + 8580 \, a b^{7} x^{21} + 25740 \, a^{2} b^{6} x^{18} + 45045 \, a^{3} b^{5} x^{15} + 50050 \, a^{4} b^{4} x^{12} + 36036 \, a^{5} b^{3} x^{9} + 16380 \, a^{6} b^{2} x^{6} + 4290 \, a^{7} b x^{3} + 495 \, a^{8}}{19305 \, x^{39}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^40,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204735, size = 124, normalized size = 1.17 \[ -\frac{1287 \, b^{8} x^{24} + 8580 \, a b^{7} x^{21} + 25740 \, a^{2} b^{6} x^{18} + 45045 \, a^{3} b^{5} x^{15} + 50050 \, a^{4} b^{4} x^{12} + 36036 \, a^{5} b^{3} x^{9} + 16380 \, a^{6} b^{2} x^{6} + 4290 \, a^{7} b x^{3} + 495 \, a^{8}}{19305 \, x^{39}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^40,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.49634, size = 99, normalized size = 0.93 \[ - \frac{495 a^{8} + 4290 a^{7} b x^{3} + 16380 a^{6} b^{2} x^{6} + 36036 a^{5} b^{3} x^{9} + 50050 a^{4} b^{4} x^{12} + 45045 a^{3} b^{5} x^{15} + 25740 a^{2} b^{6} x^{18} + 8580 a b^{7} x^{21} + 1287 b^{8} x^{24}}{19305 x^{39}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**8/x**40,x)
[Out]
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GIAC/XCAS [A] time = 0.217514, size = 124, normalized size = 1.17 \[ -\frac{1287 \, b^{8} x^{24} + 8580 \, a b^{7} x^{21} + 25740 \, a^{2} b^{6} x^{18} + 45045 \, a^{3} b^{5} x^{15} + 50050 \, a^{4} b^{4} x^{12} + 36036 \, a^{5} b^{3} x^{9} + 16380 \, a^{6} b^{2} x^{6} + 4290 \, a^{7} b x^{3} + 495 \, a^{8}}{19305 \, x^{39}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^40,x, algorithm="giac")
[Out]