Optimal. Leaf size=102 \[ -\frac{a^8}{9 x^9}-\frac{8 a^7 b}{7 x^7}-\frac{28 a^6 b^2}{5 x^5}-\frac{56 a^5 b^3}{3 x^3}-\frac{70 a^4 b^4}{x}+56 a^3 b^5 x+\frac{28}{3} a^2 b^6 x^3+\frac{8}{5} a b^7 x^5+\frac{b^8 x^7}{7} \]
[Out]
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Rubi [A] time = 0.105443, antiderivative size = 102, 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 \[ -\frac{a^8}{9 x^9}-\frac{8 a^7 b}{7 x^7}-\frac{28 a^6 b^2}{5 x^5}-\frac{56 a^5 b^3}{3 x^3}-\frac{70 a^4 b^4}{x}+56 a^3 b^5 x+\frac{28}{3} a^2 b^6 x^3+\frac{8}{5} a b^7 x^5+\frac{b^8 x^7}{7} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^8/x^10,x]
[Out]
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Rubi in Sympy [A] time = 19.801, size = 100, normalized size = 0.98 \[ - \frac{a^{8}}{9 x^{9}} - \frac{8 a^{7} b}{7 x^{7}} - \frac{28 a^{6} b^{2}}{5 x^{5}} - \frac{56 a^{5} b^{3}}{3 x^{3}} - \frac{70 a^{4} b^{4}}{x} + 56 a^{3} b^{5} x + \frac{28 a^{2} b^{6} x^{3}}{3} + \frac{8 a b^{7} x^{5}}{5} + \frac{b^{8} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**8/x**10,x)
[Out]
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Mathematica [A] time = 0.0217153, size = 102, normalized size = 1. \[ -\frac{a^8}{9 x^9}-\frac{8 a^7 b}{7 x^7}-\frac{28 a^6 b^2}{5 x^5}-\frac{56 a^5 b^3}{3 x^3}-\frac{70 a^4 b^4}{x}+56 a^3 b^5 x+\frac{28}{3} a^2 b^6 x^3+\frac{8}{5} a b^7 x^5+\frac{b^8 x^7}{7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^8/x^10,x]
[Out]
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Maple [A] time = 0.009, size = 89, normalized size = 0.9 \[ -{\frac{{a}^{8}}{9\,{x}^{9}}}-{\frac{8\,{a}^{7}b}{7\,{x}^{7}}}-{\frac{28\,{a}^{6}{b}^{2}}{5\,{x}^{5}}}-{\frac{56\,{a}^{5}{b}^{3}}{3\,{x}^{3}}}-70\,{\frac{{a}^{4}{b}^{4}}{x}}+56\,{a}^{3}{b}^{5}x+{\frac{28\,{a}^{2}{b}^{6}{x}^{3}}{3}}+{\frac{8\,a{b}^{7}{x}^{5}}{5}}+{\frac{{b}^{8}{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^8/x^10,x)
[Out]
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Maxima [A] time = 1.32951, size = 123, normalized size = 1.21 \[ \frac{1}{7} \, b^{8} x^{7} + \frac{8}{5} \, a b^{7} x^{5} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 56 \, a^{3} b^{5} x - \frac{22050 \, a^{4} b^{4} x^{8} + 5880 \, a^{5} b^{3} x^{6} + 1764 \, a^{6} b^{2} x^{4} + 360 \, a^{7} b x^{2} + 35 \, a^{8}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.195142, size = 124, normalized size = 1.22 \[ \frac{45 \, b^{8} x^{16} + 504 \, a b^{7} x^{14} + 2940 \, a^{2} b^{6} x^{12} + 17640 \, a^{3} b^{5} x^{10} - 22050 \, a^{4} b^{4} x^{8} - 5880 \, a^{5} b^{3} x^{6} - 1764 \, a^{6} b^{2} x^{4} - 360 \, a^{7} b x^{2} - 35 \, a^{8}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^10,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.22866, size = 99, normalized size = 0.97 \[ 56 a^{3} b^{5} x + \frac{28 a^{2} b^{6} x^{3}}{3} + \frac{8 a b^{7} x^{5}}{5} + \frac{b^{8} x^{7}}{7} - \frac{35 a^{8} + 360 a^{7} b x^{2} + 1764 a^{6} b^{2} x^{4} + 5880 a^{5} b^{3} x^{6} + 22050 a^{4} b^{4} x^{8}}{315 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**8/x**10,x)
[Out]
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GIAC/XCAS [A] time = 0.211474, size = 123, normalized size = 1.21 \[ \frac{1}{7} \, b^{8} x^{7} + \frac{8}{5} \, a b^{7} x^{5} + \frac{28}{3} \, a^{2} b^{6} x^{3} + 56 \, a^{3} b^{5} x - \frac{22050 \, a^{4} b^{4} x^{8} + 5880 \, a^{5} b^{3} x^{6} + 1764 \, a^{6} b^{2} x^{4} + 360 \, a^{7} b x^{2} + 35 \, a^{8}}{315 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^8/x^10,x, algorithm="giac")
[Out]