Optimal. Leaf size=18 \[ \frac{1}{3} (x-1)^{3/2} (x+1)^{3/2} \]
[Out]
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Rubi [A] time = 0.00877585, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{1}{3} (x-1)^{3/2} (x+1)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[-1 + x]*x*Sqrt[1 + x],x]
[Out]
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Rubi in Sympy [A] time = 1.91793, size = 14, normalized size = 0.78 \[ \frac{\left (x - 1\right )^{\frac{3}{2}} \left (x + 1\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(-1+x)**(1/2)*(1+x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0113245, size = 18, normalized size = 1. \[ \frac{1}{3} (x-1)^{3/2} (x+1)^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[-1 + x]*x*Sqrt[1 + x],x]
[Out]
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Maple [A] time = 0.004, size = 13, normalized size = 0.7 \[{\frac{1}{3} \left ( -1+x \right ) ^{{\frac{3}{2}}} \left ( 1+x \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(-1+x)^(1/2)*(1+x)^(1/2),x)
[Out]
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Maxima [A] time = 1.35172, size = 12, normalized size = 0.67 \[ \frac{1}{3} \,{\left (x^{2} - 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)*sqrt(x - 1)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229816, size = 101, normalized size = 5.61 \[ -\frac{4 \, x^{6} - 9 \, x^{4} -{\left (4 \, x^{5} - 7 \, x^{3} + 3 \, x\right )} \sqrt{x + 1} \sqrt{x - 1} + 6 \, x^{2} - 1}{3 \,{\left (4 \, x^{3} -{\left (4 \, x^{2} - 1\right )} \sqrt{x + 1} \sqrt{x - 1} - 3 \, x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)*sqrt(x - 1)*x,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int x \sqrt{x - 1} \sqrt{x + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(-1+x)**(1/2)*(1+x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.232017, size = 16, normalized size = 0.89 \[ \frac{1}{3} \,{\left (x + 1\right )}^{\frac{3}{2}}{\left (x - 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)*sqrt(x - 1)*x,x, algorithm="giac")
[Out]