Optimal. Leaf size=21 \[ \frac{2}{3} a x^{3/2}+\frac{2}{7} b x^{7/2} \]
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Rubi [A] time = 0.0139615, 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 \[ \frac{2}{3} a x^{3/2}+\frac{2}{7} b x^{7/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*(a + b*x^2),x]
[Out]
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Rubi in Sympy [A] time = 2.98048, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 b x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)*x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00835316, size = 21, normalized size = 1. \[ \frac{2}{3} a x^{3/2}+\frac{2}{7} b x^{7/2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*(a + b*x^2),x]
[Out]
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Maple [A] time = 0.003, size = 16, normalized size = 0.8 \[{\frac{6\,b{x}^{2}+14\,a}{21}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)*x^(1/2),x)
[Out]
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Maxima [A] time = 1.3426, size = 18, normalized size = 0.86 \[ \frac{2}{7} \, b x^{\frac{7}{2}} + \frac{2}{3} \, a x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)*sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228766, size = 22, normalized size = 1.05 \[ \frac{2}{21} \,{\left (3 \, b x^{3} + 7 \, a x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)*sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.48117, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 b x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)*x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.206018, size = 18, normalized size = 0.86 \[ \frac{2}{7} \, b x^{\frac{7}{2}} + \frac{2}{3} \, a x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)*sqrt(x),x, algorithm="giac")
[Out]