Optimal. Leaf size=21 \[ \frac{2}{3} a x^{3/2}+\frac{2}{5} b x^{5/2} \]
[Out]
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Rubi [A] time = 0.0124579, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{2}{3} a x^{3/2}+\frac{2}{5} b x^{5/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[x]*(a + b*x),x]
[Out]
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Rubi in Sympy [A] time = 2.33767, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 b x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)*x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00488006, size = 17, normalized size = 0.81 \[ \frac{2}{15} x^{3/2} (5 a+3 b x) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[x]*(a + b*x),x]
[Out]
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Maple [A] time = 0.004, size = 14, normalized size = 0.7 \[{\frac{6\,bx+10\,a}{15}{x}^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)*x^(1/2),x)
[Out]
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Maxima [A] time = 1.34221, size = 18, normalized size = 0.86 \[ \frac{2}{5} \, b x^{\frac{5}{2}} + \frac{2}{3} \, a x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207749, size = 22, normalized size = 1.05 \[ \frac{2}{15} \,{\left (3 \, b x^{2} + 5 \, a x\right )} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.6827, size = 19, normalized size = 0.9 \[ \frac{2 a x^{\frac{3}{2}}}{3} + \frac{2 b x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)*x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.201202, size = 18, normalized size = 0.86 \[ \frac{2}{5} \, b x^{\frac{5}{2}} + \frac{2}{3} \, a x^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*sqrt(x),x, algorithm="giac")
[Out]