Optimal. Leaf size=110 \[ -\frac{a^5 \left (a+b x^3\right )^9}{27 b^6}+\frac{a^4 \left (a+b x^3\right )^{10}}{6 b^6}-\frac{10 a^3 \left (a+b x^3\right )^{11}}{33 b^6}+\frac{5 a^2 \left (a+b x^3\right )^{12}}{18 b^6}+\frac{\left (a+b x^3\right )^{14}}{42 b^6}-\frac{5 a \left (a+b x^3\right )^{13}}{39 b^6} \]
[Out]
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Rubi [A] time = 0.346615, antiderivative size = 110, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^5 \left (a+b x^3\right )^9}{27 b^6}+\frac{a^4 \left (a+b x^3\right )^{10}}{6 b^6}-\frac{10 a^3 \left (a+b x^3\right )^{11}}{33 b^6}+\frac{5 a^2 \left (a+b x^3\right )^{12}}{18 b^6}+\frac{\left (a+b x^3\right )^{14}}{42 b^6}-\frac{5 a \left (a+b x^3\right )^{13}}{39 b^6} \]
Antiderivative was successfully verified.
[In] Int[x^17*(a + b*x^3)^8,x]
[Out]
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Rubi in Sympy [A] time = 27.7336, size = 100, normalized size = 0.91 \[ - \frac{a^{5} \left (a + b x^{3}\right )^{9}}{27 b^{6}} + \frac{a^{4} \left (a + b x^{3}\right )^{10}}{6 b^{6}} - \frac{10 a^{3} \left (a + b x^{3}\right )^{11}}{33 b^{6}} + \frac{5 a^{2} \left (a + b x^{3}\right )^{12}}{18 b^{6}} - \frac{5 a \left (a + b x^{3}\right )^{13}}{39 b^{6}} + \frac{\left (a + b x^{3}\right )^{14}}{42 b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**17*(b*x**3+a)**8,x)
[Out]
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Mathematica [A] time = 0.00473479, size = 108, normalized size = 0.98 \[ \frac{a^8 x^{18}}{18}+\frac{8}{21} a^7 b x^{21}+\frac{7}{6} a^6 b^2 x^{24}+\frac{56}{27} a^5 b^3 x^{27}+\frac{7}{3} a^4 b^4 x^{30}+\frac{56}{33} a^3 b^5 x^{33}+\frac{7}{9} a^2 b^6 x^{36}+\frac{8}{39} a b^7 x^{39}+\frac{b^8 x^{42}}{42} \]
Antiderivative was successfully verified.
[In] Integrate[x^17*(a + b*x^3)^8,x]
[Out]
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Maple [A] time = 0.003, size = 91, normalized size = 0.8 \[{\frac{{b}^{8}{x}^{42}}{42}}+{\frac{8\,a{b}^{7}{x}^{39}}{39}}+{\frac{7\,{a}^{2}{b}^{6}{x}^{36}}{9}}+{\frac{56\,{a}^{3}{b}^{5}{x}^{33}}{33}}+{\frac{7\,{a}^{4}{b}^{4}{x}^{30}}{3}}+{\frac{56\,{a}^{5}{b}^{3}{x}^{27}}{27}}+{\frac{7\,{a}^{6}{b}^{2}{x}^{24}}{6}}+{\frac{8\,{a}^{7}b{x}^{21}}{21}}+{\frac{{a}^{8}{x}^{18}}{18}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^17*(b*x^3+a)^8,x)
[Out]
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Maxima [A] time = 1.43434, size = 122, normalized size = 1.11 \[ \frac{1}{42} \, b^{8} x^{42} + \frac{8}{39} \, a b^{7} x^{39} + \frac{7}{9} \, a^{2} b^{6} x^{36} + \frac{56}{33} \, a^{3} b^{5} x^{33} + \frac{7}{3} \, a^{4} b^{4} x^{30} + \frac{56}{27} \, a^{5} b^{3} x^{27} + \frac{7}{6} \, a^{6} b^{2} x^{24} + \frac{8}{21} \, a^{7} b x^{21} + \frac{1}{18} \, a^{8} x^{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8*x^17,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.192949, size = 1, normalized size = 0.01 \[ \frac{1}{42} x^{42} b^{8} + \frac{8}{39} x^{39} b^{7} a + \frac{7}{9} x^{36} b^{6} a^{2} + \frac{56}{33} x^{33} b^{5} a^{3} + \frac{7}{3} x^{30} b^{4} a^{4} + \frac{56}{27} x^{27} b^{3} a^{5} + \frac{7}{6} x^{24} b^{2} a^{6} + \frac{8}{21} x^{21} b a^{7} + \frac{1}{18} x^{18} a^{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8*x^17,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.162676, size = 107, normalized size = 0.97 \[ \frac{a^{8} x^{18}}{18} + \frac{8 a^{7} b x^{21}}{21} + \frac{7 a^{6} b^{2} x^{24}}{6} + \frac{56 a^{5} b^{3} x^{27}}{27} + \frac{7 a^{4} b^{4} x^{30}}{3} + \frac{56 a^{3} b^{5} x^{33}}{33} + \frac{7 a^{2} b^{6} x^{36}}{9} + \frac{8 a b^{7} x^{39}}{39} + \frac{b^{8} x^{42}}{42} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**17*(b*x**3+a)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.21549, size = 122, normalized size = 1.11 \[ \frac{1}{42} \, b^{8} x^{42} + \frac{8}{39} \, a b^{7} x^{39} + \frac{7}{9} \, a^{2} b^{6} x^{36} + \frac{56}{33} \, a^{3} b^{5} x^{33} + \frac{7}{3} \, a^{4} b^{4} x^{30} + \frac{56}{27} \, a^{5} b^{3} x^{27} + \frac{7}{6} \, a^{6} b^{2} x^{24} + \frac{8}{21} \, a^{7} b x^{21} + \frac{1}{18} \, a^{8} x^{18} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^3 + a)^8*x^17,x, algorithm="giac")
[Out]