Optimal. Leaf size=13 \[ \frac{1}{3} (2 x+1)^{3/2} \]
[Out]
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Rubi [A] time = 0.00507333, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \frac{1}{3} (2 x+1)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 + 2*x],x]
[Out]
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Rubi in Sympy [A] time = 0.517797, size = 8, normalized size = 0.62 \[ \frac{\left (2 x + 1\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00289457, size = 13, normalized size = 1. \[ \frac{1}{3} (2 x+1)^{3/2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 + 2*x],x]
[Out]
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Maple [A] time = 0.264, size = 10, normalized size = 0.8 \[{\frac{1}{3} \left ( 1+2\,x \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.3247, size = 12, normalized size = 0.92 \[ \frac{1}{3} \,{\left (2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208579, size = 12, normalized size = 0.92 \[ \frac{1}{3} \,{\left (2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.031499, size = 8, normalized size = 0.62 \[ \frac{\left (2 x + 1\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.231308, size = 12, normalized size = 0.92 \[ \frac{1}{3} \,{\left (2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(2*x + 1),x, algorithm="giac")
[Out]