Optimal. Leaf size=62 \[ -\frac{b^2 \left (a+b x^3\right )^9}{1485 a^3 x^{27}}+\frac{b \left (a+b x^3\right )^9}{165 a^2 x^{30}}-\frac{\left (a+b x^3\right )^9}{33 a x^{33}} \]
[Out]
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Rubi [A] time = 0.0783642, antiderivative size = 62, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{b^2 \left (a+b x^3\right )^9}{1485 a^3 x^{27}}+\frac{b \left (a+b x^3\right )^9}{165 a^2 x^{30}}-\frac{\left (a+b x^3\right )^9}{33 a x^{33}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^3)^8/x^34,x]
[Out]
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Rubi in Sympy [A] time = 8.76503, size = 53, normalized size = 0.85 \[ - \frac{\left (a + b x^{3}\right )^{9}}{33 a x^{33}} + \frac{b \left (a + b x^{3}\right )^{9}}{165 a^{2} x^{30}} - \frac{b^{2} \left (a + b x^{3}\right )^{9}}{1485 a^{3} x^{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**3+a)**8/x**34,x)
[Out]
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Mathematica [A] time = 0.0178311, size = 108, normalized size = 1.74 \[ -\frac{a^8}{33 x^{33}}-\frac{4 a^7 b}{15 x^{30}}-\frac{28 a^6 b^2}{27 x^{27}}-\frac{7 a^5 b^3}{3 x^{24}}-\frac{10 a^4 b^4}{3 x^{21}}-\frac{28 a^3 b^5}{9 x^{18}}-\frac{28 a^2 b^6}{15 x^{15}}-\frac{2 a b^7}{3 x^{12}}-\frac{b^8}{9 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^3)^8/x^34,x]
[Out]
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Maple [A] time = 0.01, size = 91, normalized size = 1.5 \[ -{\frac{2\,a{b}^{7}}{3\,{x}^{12}}}-{\frac{28\,{a}^{2}{b}^{6}}{15\,{x}^{15}}}-{\frac{28\,{a}^{6}{b}^{2}}{27\,{x}^{27}}}-{\frac{10\,{a}^{4}{b}^{4}}{3\,{x}^{21}}}-{\frac{{a}^{8}}{33\,{x}^{33}}}-{\frac{7\,{a}^{5}{b}^{3}}{3\,{x}^{24}}}-{\frac{{b}^{8}}{9\,{x}^{9}}}-{\frac{4\,{a}^{7}b}{15\,{x}^{30}}}-{\frac{28\,{a}^{3}{b}^{5}}{9\,{x}^{18}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^3+a)^8/x^34,x)
[Out]
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Maxima [A] time = 1.43362, size = 124, normalized size = 2. \[ -\frac{165 \, b^{8} x^{24} + 990 \, a b^{7} x^{21} + 2772 \, a^{2} b^{6} x^{18} + 4620 \, a^{3} b^{5} x^{15} + 4950 \, a^{4} b^{4} x^{12} + 3465 \, a^{5} b^{3} x^{9} + 1540 \, a^{6} b^{2} x^{6} + 396 \, a^{7} b x^{3} + 45 \, a^{8}}{1485 \, x^{33}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^34,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202246, size = 124, normalized size = 2. \[ -\frac{165 \, b^{8} x^{24} + 990 \, a b^{7} x^{21} + 2772 \, a^{2} b^{6} x^{18} + 4620 \, a^{3} b^{5} x^{15} + 4950 \, a^{4} b^{4} x^{12} + 3465 \, a^{5} b^{3} x^{9} + 1540 \, a^{6} b^{2} x^{6} + 396 \, a^{7} b x^{3} + 45 \, a^{8}}{1485 \, x^{33}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^34,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.7222, size = 99, normalized size = 1.6 \[ - \frac{45 a^{8} + 396 a^{7} b x^{3} + 1540 a^{6} b^{2} x^{6} + 3465 a^{5} b^{3} x^{9} + 4950 a^{4} b^{4} x^{12} + 4620 a^{3} b^{5} x^{15} + 2772 a^{2} b^{6} x^{18} + 990 a b^{7} x^{21} + 165 b^{8} x^{24}}{1485 x^{33}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**3+a)**8/x**34,x)
[Out]
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GIAC/XCAS [A] time = 0.218899, size = 124, normalized size = 2. \[ -\frac{165 \, b^{8} x^{24} + 990 \, a b^{7} x^{21} + 2772 \, a^{2} b^{6} x^{18} + 4620 \, a^{3} b^{5} x^{15} + 4950 \, a^{4} b^{4} x^{12} + 3465 \, a^{5} b^{3} x^{9} + 1540 \, a^{6} b^{2} x^{6} + 396 \, a^{7} b x^{3} + 45 \, a^{8}}{1485 \, x^{33}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8/x^34,x, algorithm="giac")
[Out]