Optimal. Leaf size=51 \[ \frac{2}{21} b^3 x^{21/2}+\frac{6}{25} b^2 c x^{25/2}+\frac{6}{29} b c^2 x^{29/2}+\frac{2}{33} c^3 x^{33/2} \]
[Out]
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Rubi [A] time = 0.0474317, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{2}{21} b^3 x^{21/2}+\frac{6}{25} b^2 c x^{25/2}+\frac{6}{29} b c^2 x^{29/2}+\frac{2}{33} c^3 x^{33/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(b*x^2 + c*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 8.19082, size = 49, normalized size = 0.96 \[ \frac{2 b^{3} x^{\frac{21}{2}}}{21} + \frac{6 b^{2} c x^{\frac{25}{2}}}{25} + \frac{6 b c^{2} x^{\frac{29}{2}}}{29} + \frac{2 c^{3} x^{\frac{33}{2}}}{33} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(c*x**4+b*x**2)**3,x)
[Out]
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Mathematica [A] time = 0.0172375, size = 51, normalized size = 1. \[ \frac{2}{21} b^3 x^{21/2}+\frac{6}{25} b^2 c x^{25/2}+\frac{6}{29} b c^2 x^{29/2}+\frac{2}{33} c^3 x^{33/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(b*x^2 + c*x^4)^3,x]
[Out]
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Maple [A] time = 0.007, size = 38, normalized size = 0.8 \[{\frac{10150\,{c}^{3}{x}^{6}+34650\,b{c}^{2}{x}^{4}+40194\,{b}^{2}c{x}^{2}+15950\,{b}^{3}}{167475}{x}^{{\frac{21}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(c*x^4+b*x^2)^3,x)
[Out]
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Maxima [A] time = 0.709979, size = 47, normalized size = 0.92 \[ \frac{2}{33} \, c^{3} x^{\frac{33}{2}} + \frac{6}{29} \, b c^{2} x^{\frac{29}{2}} + \frac{6}{25} \, b^{2} c x^{\frac{25}{2}} + \frac{2}{21} \, b^{3} x^{\frac{21}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3*x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.270673, size = 54, normalized size = 1.06 \[ \frac{2}{167475} \,{\left (5075 \, c^{3} x^{16} + 17325 \, b c^{2} x^{14} + 20097 \, b^{2} c x^{12} + 7975 \, b^{3} x^{10}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3*x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(c*x**4+b*x**2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.26906, size = 47, normalized size = 0.92 \[ \frac{2}{33} \, c^{3} x^{\frac{33}{2}} + \frac{6}{29} \, b c^{2} x^{\frac{29}{2}} + \frac{6}{25} \, b^{2} c x^{\frac{25}{2}} + \frac{2}{21} \, b^{3} x^{\frac{21}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + b*x^2)^3*x^(7/2),x, algorithm="giac")
[Out]