Optimal. Leaf size=65 \[ -\frac{a^5}{11 x^{11}}-\frac{5 a^4 b}{9 x^9}-\frac{10 a^3 b^2}{7 x^7}-\frac{2 a^2 b^3}{x^5}-\frac{5 a b^4}{3 x^3}-\frac{b^5}{x} \]
[Out]
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Rubi [A] time = 0.0640907, antiderivative size = 65, 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 \[ -\frac{a^5}{11 x^{11}}-\frac{5 a^4 b}{9 x^9}-\frac{10 a^3 b^2}{7 x^7}-\frac{2 a^2 b^3}{x^5}-\frac{5 a b^4}{3 x^3}-\frac{b^5}{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^5/x^12,x]
[Out]
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Rubi in Sympy [A] time = 12.106, size = 63, normalized size = 0.97 \[ - \frac{a^{5}}{11 x^{11}} - \frac{5 a^{4} b}{9 x^{9}} - \frac{10 a^{3} b^{2}}{7 x^{7}} - \frac{2 a^{2} b^{3}}{x^{5}} - \frac{5 a b^{4}}{3 x^{3}} - \frac{b^{5}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**5/x**12,x)
[Out]
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Mathematica [A] time = 0.00754584, size = 65, normalized size = 1. \[ -\frac{a^5}{11 x^{11}}-\frac{5 a^4 b}{9 x^9}-\frac{10 a^3 b^2}{7 x^7}-\frac{2 a^2 b^3}{x^5}-\frac{5 a b^4}{3 x^3}-\frac{b^5}{x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^5/x^12,x]
[Out]
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Maple [A] time = 0.008, size = 58, normalized size = 0.9 \[ -{\frac{{a}^{5}}{11\,{x}^{11}}}-{\frac{5\,{a}^{4}b}{9\,{x}^{9}}}-{\frac{10\,{a}^{3}{b}^{2}}{7\,{x}^{7}}}-2\,{\frac{{a}^{2}{b}^{3}}{{x}^{5}}}-{\frac{5\,a{b}^{4}}{3\,{x}^{3}}}-{\frac{{b}^{5}}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^5/x^12,x)
[Out]
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Maxima [A] time = 1.34133, size = 80, normalized size = 1.23 \[ -\frac{693 \, b^{5} x^{10} + 1155 \, a b^{4} x^{8} + 1386 \, a^{2} b^{3} x^{6} + 990 \, a^{3} b^{2} x^{4} + 385 \, a^{4} b x^{2} + 63 \, a^{5}}{693 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5/x^12,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.195432, size = 80, normalized size = 1.23 \[ -\frac{693 \, b^{5} x^{10} + 1155 \, a b^{4} x^{8} + 1386 \, a^{2} b^{3} x^{6} + 990 \, a^{3} b^{2} x^{4} + 385 \, a^{4} b x^{2} + 63 \, a^{5}}{693 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5/x^12,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.23197, size = 63, normalized size = 0.97 \[ - \frac{63 a^{5} + 385 a^{4} b x^{2} + 990 a^{3} b^{2} x^{4} + 1386 a^{2} b^{3} x^{6} + 1155 a b^{4} x^{8} + 693 b^{5} x^{10}}{693 x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**5/x**12,x)
[Out]
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GIAC/XCAS [A] time = 0.206826, size = 80, normalized size = 1.23 \[ -\frac{693 \, b^{5} x^{10} + 1155 \, a b^{4} x^{8} + 1386 \, a^{2} b^{3} x^{6} + 990 \, a^{3} b^{2} x^{4} + 385 \, a^{4} b x^{2} + 63 \, a^{5}}{693 \, x^{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^5/x^12,x, algorithm="giac")
[Out]