Optimal. Leaf size=27 \[ \frac{5}{6} (1-2 x)^{3/2}-\frac{11}{2} \sqrt{1-2 x} \]
[Out]
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Rubi [A] time = 0.0218363, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{5}{6} (1-2 x)^{3/2}-\frac{11}{2} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 3.75337, size = 22, normalized size = 0.81 \[ \frac{5 \left (- 2 x + 1\right )^{\frac{3}{2}}}{6} - \frac{11 \sqrt{- 2 x + 1}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00588417, size = 18, normalized size = 0.67 \[ -\frac{1}{3} \sqrt{1-2 x} (5 x+14) \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.004, size = 15, normalized size = 0.6 \[ -{\frac{14+5\,x}{3}\sqrt{1-2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.34606, size = 26, normalized size = 0.96 \[ \frac{5}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{11}{2} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206348, size = 19, normalized size = 0.7 \[ -\frac{1}{3} \,{\left (5 \, x + 14\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.54853, size = 88, normalized size = 3.26 \[ \begin{cases} - \frac{\sqrt{5} i \left (x + \frac{3}{5}\right ) \sqrt{10 x - 5}}{3} - \frac{11 \sqrt{5} i \sqrt{10 x - 5}}{15} & \text{for}\: \frac{10 \left |{x + \frac{3}{5}}\right |}{11} > 1 \\- \frac{\sqrt{5} \sqrt{- 10 x + 5} \left (x + \frac{3}{5}\right )}{3} - \frac{11 \sqrt{5} \sqrt{- 10 x + 5}}{15} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.207046, size = 26, normalized size = 0.96 \[ \frac{5}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{11}{2} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/sqrt(-2*x + 1),x, algorithm="giac")
[Out]