Optimal. Leaf size=13 \[ \frac{1}{3} \left (x^2+1\right )^{3/2} \]
[Out]
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Rubi [A] time = 0.00497958, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{1}{3} \left (x^2+1\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Int[x*Sqrt[1 + x^2],x]
[Out]
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Rubi in Sympy [A] time = 0.76266, size = 8, normalized size = 0.62 \[ \frac{\left (x^{2} + 1\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(x**2+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00328751, size = 13, normalized size = 1. \[ \frac{1}{3} \left (x^2+1\right )^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[x*Sqrt[1 + x^2],x]
[Out]
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Maple [A] time = 0.003, size = 10, normalized size = 0.8 \[{\frac{1}{3} \left ({x}^{2}+1 \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(x^2+1)^(1/2),x)
[Out]
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Maxima [A] time = 1.34017, size = 12, normalized size = 0.92 \[ \frac{1}{3} \,{\left (x^{2} + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^2 + 1)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234433, size = 93, normalized size = 7.15 \[ -\frac{4 \, x^{6} + 9 \, x^{4} + 6 \, x^{2} -{\left (4 \, x^{5} + 7 \, x^{3} + 3 \, x\right )} \sqrt{x^{2} + 1} + 1}{3 \,{\left (4 \, x^{3} -{\left (4 \, x^{2} + 1\right )} \sqrt{x^{2} + 1} + 3 \, x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^2 + 1)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.216007, size = 22, normalized size = 1.69 \[ \frac{x^{2} \sqrt{x^{2} + 1}}{3} + \frac{\sqrt{x^{2} + 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(x**2+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.203724, size = 12, normalized size = 0.92 \[ \frac{1}{3} \,{\left (x^{2} + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^2 + 1)*x,x, algorithm="giac")
[Out]