Optimal. Leaf size=21 \[ \frac{2}{9} a x^{9/2}+\frac{2}{13} b x^{13/2} \]
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Rubi [A] time = 0.0137314, antiderivative size = 21, 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 \[ \frac{2}{9} a x^{9/2}+\frac{2}{13} b x^{13/2} \]
Antiderivative was successfully verified.
[In] Int[x^(7/2)*(a + b*x^2),x]
[Out]
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Rubi in Sympy [A] time = 2.9219, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{9}{2}}}{9} + \frac{2 b x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(7/2)*(b*x**2+a),x)
[Out]
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Mathematica [A] time = 0.00804533, size = 21, normalized size = 1. \[ \frac{2}{9} a x^{9/2}+\frac{2}{13} b x^{13/2} \]
Antiderivative was successfully verified.
[In] Integrate[x^(7/2)*(a + b*x^2),x]
[Out]
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Maple [A] time = 0.004, size = 16, normalized size = 0.8 \[{\frac{18\,b{x}^{2}+26\,a}{117}{x}^{{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(7/2)*(b*x^2+a),x)
[Out]
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Maxima [A] time = 1.34918, size = 18, normalized size = 0.86 \[ \frac{2}{13} \, b x^{\frac{13}{2}} + \frac{2}{9} \, a x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)*x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217804, size = 24, normalized size = 1.14 \[ \frac{2}{117} \,{\left (9 \, b x^{6} + 13 \, a x^{4}\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)*x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 19.8947, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{9}{2}}}{9} + \frac{2 b x^{\frac{13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(7/2)*(b*x**2+a),x)
[Out]
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GIAC/XCAS [A] time = 0.205132, size = 18, normalized size = 0.86 \[ \frac{2}{13} \, b x^{\frac{13}{2}} + \frac{2}{9} \, a x^{\frac{9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)*x^(7/2),x, algorithm="giac")
[Out]