Optimal. Leaf size=99 \[ -\frac{a^8}{15 x^{15}}-\frac{8 a^7 b}{13 x^{13}}-\frac{28 a^6 b^2}{11 x^{11}}-\frac{56 a^5 b^3}{9 x^9}-\frac{10 a^4 b^4}{x^7}-\frac{56 a^3 b^5}{5 x^5}-\frac{28 a^2 b^6}{3 x^3}-\frac{8 a b^7}{x}+b^8 x \]
[Out]
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Rubi [A] time = 0.107473, antiderivative size = 99, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{a^8}{15 x^{15}}-\frac{8 a^7 b}{13 x^{13}}-\frac{28 a^6 b^2}{11 x^{11}}-\frac{56 a^5 b^3}{9 x^9}-\frac{10 a^4 b^4}{x^7}-\frac{56 a^3 b^5}{5 x^5}-\frac{28 a^2 b^6}{3 x^3}-\frac{8 a b^7}{x}+b^8 x \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^8/x^16,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{8}}{15 x^{15}} - \frac{8 a^{7} b}{13 x^{13}} - \frac{28 a^{6} b^{2}}{11 x^{11}} - \frac{56 a^{5} b^{3}}{9 x^{9}} - \frac{10 a^{4} b^{4}}{x^{7}} - \frac{56 a^{3} b^{5}}{5 x^{5}} - \frac{28 a^{2} b^{6}}{3 x^{3}} - \frac{8 a b^{7}}{x} + \int b^{8}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**8/x**16,x)
[Out]
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Mathematica [A] time = 0.00982412, size = 99, normalized size = 1. \[ -\frac{a^8}{15 x^{15}}-\frac{8 a^7 b}{13 x^{13}}-\frac{28 a^6 b^2}{11 x^{11}}-\frac{56 a^5 b^3}{9 x^9}-\frac{10 a^4 b^4}{x^7}-\frac{56 a^3 b^5}{5 x^5}-\frac{28 a^2 b^6}{3 x^3}-\frac{8 a b^7}{x}+b^8 x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^8/x^16,x]
[Out]
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Maple [A] time = 0.01, size = 88, normalized size = 0.9 \[ -{\frac{{a}^{8}}{15\,{x}^{15}}}-{\frac{8\,{a}^{7}b}{13\,{x}^{13}}}-{\frac{28\,{a}^{6}{b}^{2}}{11\,{x}^{11}}}-{\frac{56\,{a}^{5}{b}^{3}}{9\,{x}^{9}}}-10\,{\frac{{a}^{4}{b}^{4}}{{x}^{7}}}-{\frac{56\,{a}^{3}{b}^{5}}{5\,{x}^{5}}}-{\frac{28\,{a}^{2}{b}^{6}}{3\,{x}^{3}}}-8\,{\frac{a{b}^{7}}{x}}+{b}^{8}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^8/x^16,x)
[Out]
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Maxima [A] time = 1.34659, size = 122, normalized size = 1.23 \[ b^{8} x - \frac{51480 \, a b^{7} x^{14} + 60060 \, a^{2} b^{6} x^{12} + 72072 \, a^{3} b^{5} x^{10} + 64350 \, a^{4} b^{4} x^{8} + 40040 \, a^{5} b^{3} x^{6} + 16380 \, a^{6} b^{2} x^{4} + 3960 \, a^{7} b x^{2} + 429 \, a^{8}}{6435 \, x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^16,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199813, size = 124, normalized size = 1.25 \[ \frac{6435 \, b^{8} x^{16} - 51480 \, a b^{7} x^{14} - 60060 \, a^{2} b^{6} x^{12} - 72072 \, a^{3} b^{5} x^{10} - 64350 \, a^{4} b^{4} x^{8} - 40040 \, a^{5} b^{3} x^{6} - 16380 \, a^{6} b^{2} x^{4} - 3960 \, a^{7} b x^{2} - 429 \, a^{8}}{6435 \, x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^16,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.31311, size = 94, normalized size = 0.95 \[ b^{8} x - \frac{429 a^{8} + 3960 a^{7} b x^{2} + 16380 a^{6} b^{2} x^{4} + 40040 a^{5} b^{3} x^{6} + 64350 a^{4} b^{4} x^{8} + 72072 a^{3} b^{5} x^{10} + 60060 a^{2} b^{6} x^{12} + 51480 a b^{7} x^{14}}{6435 x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**8/x**16,x)
[Out]
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GIAC/XCAS [A] time = 0.213568, size = 122, normalized size = 1.23 \[ b^{8} x - \frac{51480 \, a b^{7} x^{14} + 60060 \, a^{2} b^{6} x^{12} + 72072 \, a^{3} b^{5} x^{10} + 64350 \, a^{4} b^{4} x^{8} + 40040 \, a^{5} b^{3} x^{6} + 16380 \, a^{6} b^{2} x^{4} + 3960 \, a^{7} b x^{2} + 429 \, a^{8}}{6435 \, x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^16,x, algorithm="giac")
[Out]