Optimal. Leaf size=62 \[ -\frac{2 a^2}{5 x^{5/2}}+\frac{2}{3} x^{3/2} \left (2 a c+b^2\right )-\frac{4 a b}{\sqrt{x}}+\frac{4}{7} b c x^{7/2}+\frac{2}{11} c^2 x^{11/2} \]
[Out]
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Rubi [A] time = 0.0530036, antiderivative size = 62, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{2 a^2}{5 x^{5/2}}+\frac{2}{3} x^{3/2} \left (2 a c+b^2\right )-\frac{4 a b}{\sqrt{x}}+\frac{4}{7} b c x^{7/2}+\frac{2}{11} c^2 x^{11/2} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2 + c*x^4)^2/x^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 9.2531, size = 63, normalized size = 1.02 \[ - \frac{2 a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 a b}{\sqrt{x}} + \frac{4 b c x^{\frac{7}{2}}}{7} + \frac{2 c^{2} x^{\frac{11}{2}}}{11} + x^{\frac{3}{2}} \left (\frac{4 a c}{3} + \frac{2 b^{2}}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+b*x**2+a)**2/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.0365881, size = 50, normalized size = 0.81 \[ \frac{2 \left (-231 a^2+385 x^4 \left (2 a c+b^2\right )-2310 a b x^2+330 b c x^6+105 c^2 x^8\right )}{1155 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2 + c*x^4)^2/x^(7/2),x]
[Out]
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Maple [A] time = 0.009, size = 49, normalized size = 0.8 \[ -{\frac{-210\,{c}^{2}{x}^{8}-660\,bc{x}^{6}-1540\,{x}^{4}ac-770\,{b}^{2}{x}^{4}+4620\,ab{x}^{2}+462\,{a}^{2}}{1155}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+b*x^2+a)^2/x^(7/2),x)
[Out]
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Maxima [A] time = 0.732638, size = 61, normalized size = 0.98 \[ \frac{2}{11} \, c^{2} x^{\frac{11}{2}} + \frac{4}{7} \, b c x^{\frac{7}{2}} + \frac{2}{3} \,{\left (b^{2} + 2 \, a c\right )} x^{\frac{3}{2}} - \frac{2 \,{\left (10 \, a b x^{2} + a^{2}\right )}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.27545, size = 62, normalized size = 1. \[ \frac{2 \,{\left (105 \, c^{2} x^{8} + 330 \, b c x^{6} + 385 \,{\left (b^{2} + 2 \, a c\right )} x^{4} - 2310 \, a b x^{2} - 231 \, a^{2}\right )}}{1155 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 26.66, size = 68, normalized size = 1.1 \[ - \frac{2 a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 a b}{\sqrt{x}} + \frac{4 a c x^{\frac{3}{2}}}{3} + \frac{2 b^{2} x^{\frac{3}{2}}}{3} + \frac{4 b c x^{\frac{7}{2}}}{7} + \frac{2 c^{2} x^{\frac{11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+b*x**2+a)**2/x**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.263071, size = 63, normalized size = 1.02 \[ \frac{2}{11} \, c^{2} x^{\frac{11}{2}} + \frac{4}{7} \, b c x^{\frac{7}{2}} + \frac{2}{3} \, b^{2} x^{\frac{3}{2}} + \frac{4}{3} \, a c x^{\frac{3}{2}} - \frac{2 \,{\left (10 \, a b x^{2} + a^{2}\right )}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2 + a)^2/x^(7/2),x, algorithm="giac")
[Out]