Optimal. Leaf size=23 \[ \frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2} \]
[Out]
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Rubi [A] time = 0.0114164, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[x*Sqrt[1 + x],x]
[Out]
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Rubi in Sympy [A] time = 0.980611, size = 19, normalized size = 0.83 \[ \frac{2 \left (x + 1\right )^{\frac{5}{2}}}{5} - \frac{2 \left (x + 1\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(1+x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00503717, size = 16, normalized size = 0.7 \[ \frac{2}{15} (x+1)^{3/2} (3 x-2) \]
Antiderivative was successfully verified.
[In] Integrate[x*Sqrt[1 + x],x]
[Out]
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Maple [A] time = 0., size = 13, normalized size = 0.6 \[{\frac{-4+6\,x}{15} \left ( 1+x \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(1+x)^(1/2),x)
[Out]
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Maxima [A] time = 1.34049, size = 20, normalized size = 0.87 \[ \frac{2}{5} \,{\left (x + 1\right )}^{\frac{5}{2}} - \frac{2}{3} \,{\left (x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208882, size = 20, normalized size = 0.87 \[ \frac{2}{15} \,{\left (3 \, x^{2} + x - 2\right )} \sqrt{x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.44474, size = 34, normalized size = 1.48 \[ \frac{2 x^{2} \sqrt{x + 1}}{5} + \frac{2 x \sqrt{x + 1}}{15} - \frac{4 \sqrt{x + 1}}{15} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(1+x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.198518, size = 20, normalized size = 0.87 \[ \frac{2}{5} \,{\left (x + 1\right )}^{\frac{5}{2}} - \frac{2}{3} \,{\left (x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x + 1)*x,x, algorithm="giac")
[Out]