Optimal. Leaf size=15 \[ \frac{2}{3} (x+1)^{3/2}-x \]
[Out]
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Rubi [A] time = 0.0171658, antiderivative size = 15, 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 \[ \frac{2}{3} (x+1)^{3/2}-x \]
Antiderivative was successfully verified.
[In] Int[x/(1 + Sqrt[1 + x]),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{2 \left (x + 1\right )^{\frac{3}{2}}}{3} - 2 \int ^{\sqrt{x + 1}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(1+(1+x)**(1/2)),x)
[Out]
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Mathematica [A] time = 0.00966893, size = 15, normalized size = 1. \[ \frac{2}{3} (x+1)^{3/2}-x \]
Antiderivative was successfully verified.
[In] Integrate[x/(1 + Sqrt[1 + x]),x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \[{\frac{2}{3} \left ( 1+x \right ) ^{{\frac{3}{2}}}}-1-x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(1+(1+x)^(1/2)),x)
[Out]
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Maxima [A] time = 1.36507, size = 16, normalized size = 1.07 \[ \frac{2}{3} \,{\left (x + 1\right )}^{\frac{3}{2}} - x - 1 \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(sqrt(x + 1) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.200508, size = 15, normalized size = 1. \[ \frac{2}{3} \,{\left (x + 1\right )}^{\frac{3}{2}} - x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(sqrt(x + 1) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.3924, size = 22, normalized size = 1.47 \[ \frac{2 x \sqrt{x + 1}}{3} - x + \frac{2 \sqrt{x + 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(1+(1+x)**(1/2)),x)
[Out]
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GIAC/XCAS [A] time = 0.207377, size = 16, normalized size = 1.07 \[ \frac{2}{3} \,{\left (x + 1\right )}^{\frac{3}{2}} - x - 1 \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(sqrt(x + 1) + 1),x, algorithm="giac")
[Out]