Optimal. Leaf size=108 \[ -\frac{a^8}{30 x^{30}}-\frac{2 a^7 b}{7 x^{28}}-\frac{14 a^6 b^2}{13 x^{26}}-\frac{7 a^5 b^3}{3 x^{24}}-\frac{35 a^4 b^4}{11 x^{22}}-\frac{14 a^3 b^5}{5 x^{20}}-\frac{14 a^2 b^6}{9 x^{18}}-\frac{a b^7}{2 x^{16}}-\frac{b^8}{14 x^{14}} \]
[Out]
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Rubi [A] time = 0.13646, antiderivative size = 108, 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 \[ -\frac{a^8}{30 x^{30}}-\frac{2 a^7 b}{7 x^{28}}-\frac{14 a^6 b^2}{13 x^{26}}-\frac{7 a^5 b^3}{3 x^{24}}-\frac{35 a^4 b^4}{11 x^{22}}-\frac{14 a^3 b^5}{5 x^{20}}-\frac{14 a^2 b^6}{9 x^{18}}-\frac{a b^7}{2 x^{16}}-\frac{b^8}{14 x^{14}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^8/x^31,x]
[Out]
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Rubi in Sympy [A] time = 24.4194, size = 107, normalized size = 0.99 \[ - \frac{a^{8}}{30 x^{30}} - \frac{2 a^{7} b}{7 x^{28}} - \frac{14 a^{6} b^{2}}{13 x^{26}} - \frac{7 a^{5} b^{3}}{3 x^{24}} - \frac{35 a^{4} b^{4}}{11 x^{22}} - \frac{14 a^{3} b^{5}}{5 x^{20}} - \frac{14 a^{2} b^{6}}{9 x^{18}} - \frac{a b^{7}}{2 x^{16}} - \frac{b^{8}}{14 x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**8/x**31,x)
[Out]
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Mathematica [A] time = 0.00810901, size = 108, normalized size = 1. \[ -\frac{a^8}{30 x^{30}}-\frac{2 a^7 b}{7 x^{28}}-\frac{14 a^6 b^2}{13 x^{26}}-\frac{7 a^5 b^3}{3 x^{24}}-\frac{35 a^4 b^4}{11 x^{22}}-\frac{14 a^3 b^5}{5 x^{20}}-\frac{14 a^2 b^6}{9 x^{18}}-\frac{a b^7}{2 x^{16}}-\frac{b^8}{14 x^{14}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^8/x^31,x]
[Out]
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Maple [A] time = 0.009, size = 91, normalized size = 0.8 \[ -{\frac{{a}^{8}}{30\,{x}^{30}}}-{\frac{2\,{a}^{7}b}{7\,{x}^{28}}}-{\frac{14\,{a}^{6}{b}^{2}}{13\,{x}^{26}}}-{\frac{7\,{a}^{5}{b}^{3}}{3\,{x}^{24}}}-{\frac{35\,{a}^{4}{b}^{4}}{11\,{x}^{22}}}-{\frac{14\,{a}^{3}{b}^{5}}{5\,{x}^{20}}}-{\frac{14\,{a}^{2}{b}^{6}}{9\,{x}^{18}}}-{\frac{a{b}^{7}}{2\,{x}^{16}}}-{\frac{{b}^{8}}{14\,{x}^{14}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^8/x^31,x)
[Out]
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Maxima [A] time = 1.32672, size = 124, normalized size = 1.15 \[ -\frac{6435 \, b^{8} x^{16} + 45045 \, a b^{7} x^{14} + 140140 \, a^{2} b^{6} x^{12} + 252252 \, a^{3} b^{5} x^{10} + 286650 \, a^{4} b^{4} x^{8} + 210210 \, a^{5} b^{3} x^{6} + 97020 \, a^{6} b^{2} x^{4} + 25740 \, a^{7} b x^{2} + 3003 \, a^{8}}{90090 \, x^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^31,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.193265, size = 124, normalized size = 1.15 \[ -\frac{6435 \, b^{8} x^{16} + 45045 \, a b^{7} x^{14} + 140140 \, a^{2} b^{6} x^{12} + 252252 \, a^{3} b^{5} x^{10} + 286650 \, a^{4} b^{4} x^{8} + 210210 \, a^{5} b^{3} x^{6} + 97020 \, a^{6} b^{2} x^{4} + 25740 \, a^{7} b x^{2} + 3003 \, a^{8}}{90090 \, x^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^31,x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.58287, size = 99, normalized size = 0.92 \[ - \frac{3003 a^{8} + 25740 a^{7} b x^{2} + 97020 a^{6} b^{2} x^{4} + 210210 a^{5} b^{3} x^{6} + 286650 a^{4} b^{4} x^{8} + 252252 a^{3} b^{5} x^{10} + 140140 a^{2} b^{6} x^{12} + 45045 a b^{7} x^{14} + 6435 b^{8} x^{16}}{90090 x^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**8/x**31,x)
[Out]
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GIAC/XCAS [A] time = 0.207922, size = 124, normalized size = 1.15 \[ -\frac{6435 \, b^{8} x^{16} + 45045 \, a b^{7} x^{14} + 140140 \, a^{2} b^{6} x^{12} + 252252 \, a^{3} b^{5} x^{10} + 286650 \, a^{4} b^{4} x^{8} + 210210 \, a^{5} b^{3} x^{6} + 97020 \, a^{6} b^{2} x^{4} + 25740 \, a^{7} b x^{2} + 3003 \, a^{8}}{90090 \, x^{30}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^31,x, algorithm="giac")
[Out]