Optimal. Leaf size=53 \[ \frac{125}{56} (1-2 x)^{7/2}-\frac{165}{8} (1-2 x)^{5/2}+\frac{605}{8} (1-2 x)^{3/2}-\frac{1331}{8} \sqrt{1-2 x} \]
[Out]
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Rubi [A] time = 0.0353927, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{125}{56} (1-2 x)^{7/2}-\frac{165}{8} (1-2 x)^{5/2}+\frac{605}{8} (1-2 x)^{3/2}-\frac{1331}{8} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^3/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 6.05335, size = 46, normalized size = 0.87 \[ \frac{125 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{165 \left (- 2 x + 1\right )^{\frac{5}{2}}}{8} + \frac{605 \left (- 2 x + 1\right )^{\frac{3}{2}}}{8} - \frac{1331 \sqrt{- 2 x + 1}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**3/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0235856, size = 28, normalized size = 0.53 \[ -\frac{1}{7} \sqrt{1-2 x} \left (125 x^3+390 x^2+575 x+764\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^3/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.004, size = 25, normalized size = 0.5 \[ -{\frac{125\,{x}^{3}+390\,{x}^{2}+575\,x+764}{7}\sqrt{1-2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^3/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.35588, size = 50, normalized size = 0.94 \[ \frac{125}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{165}{8} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{605}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1331}{8} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.238393, size = 32, normalized size = 0.6 \[ -\frac{1}{7} \,{\left (125 \, x^{3} + 390 \, x^{2} + 575 \, x + 764\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.13136, size = 190, normalized size = 3.58 \[ \begin{cases} - \frac{25 \sqrt{5} i \left (x + \frac{3}{5}\right )^{3} \sqrt{10 x - 5}}{7} - \frac{33 \sqrt{5} i \left (x + \frac{3}{5}\right )^{2} \sqrt{10 x - 5}}{7} - \frac{242 \sqrt{5} i \left (x + \frac{3}{5}\right ) \sqrt{10 x - 5}}{35} - \frac{2662 \sqrt{5} i \sqrt{10 x - 5}}{175} & \text{for}\: \frac{10 \left |{x + \frac{3}{5}}\right |}{11} > 1 \\- \frac{25 \sqrt{5} \sqrt{- 10 x + 5} \left (x + \frac{3}{5}\right )^{3}}{7} - \frac{33 \sqrt{5} \sqrt{- 10 x + 5} \left (x + \frac{3}{5}\right )^{2}}{7} - \frac{242 \sqrt{5} \sqrt{- 10 x + 5} \left (x + \frac{3}{5}\right )}{35} - \frac{2662 \sqrt{5} \sqrt{- 10 x + 5}}{175} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**3/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.237445, size = 69, normalized size = 1.3 \[ -\frac{125}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{165}{8} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{605}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{1331}{8} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/sqrt(-2*x + 1),x, algorithm="giac")
[Out]