Optimal. Leaf size=53 \[ \frac{25}{8} (1-2 x)^{5/2}-\frac{275}{8} (1-2 x)^{3/2}+\frac{1815}{8} \sqrt{1-2 x}+\frac{1331}{8 \sqrt{1-2 x}} \]
[Out]
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Rubi [A] time = 0.0340452, 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 \[ \frac{25}{8} (1-2 x)^{5/2}-\frac{275}{8} (1-2 x)^{3/2}+\frac{1815}{8} \sqrt{1-2 x}+\frac{1331}{8 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^3/(1 - 2*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 5.87251, size = 46, normalized size = 0.87 \[ \frac{25 \left (- 2 x + 1\right )^{\frac{5}{2}}}{8} - \frac{275 \left (- 2 x + 1\right )^{\frac{3}{2}}}{8} + \frac{1815 \sqrt{- 2 x + 1}}{8} + \frac{1331}{8 \sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**3/(1-2*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0309894, size = 25, normalized size = 0.47 \[ \frac{-25 x^3-100 x^2-335 x+362}{\sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^3/(1 - 2*x)^(3/2),x]
[Out]
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Maple [A] time = 0.004, size = 25, normalized size = 0.5 \[ -{(25\,{x}^{3}+100\,{x}^{2}+335\,x-362){\frac{1}{\sqrt{1-2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^3/(1-2*x)^(3/2),x)
[Out]
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Maxima [A] time = 1.3444, size = 50, normalized size = 0.94 \[ \frac{25}{8} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{275}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1815}{8} \, \sqrt{-2 \, x + 1} + \frac{1331}{8 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217145, size = 32, normalized size = 0.6 \[ -\frac{25 \, x^{3} + 100 \, x^{2} + 335 \, x - 362}{\sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/(-2*x + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.38117, size = 435, normalized size = 8.21 \[ \begin{cases} \frac{125 \sqrt{55} i \left (x + \frac{3}{5}\right )^{3} \sqrt{10 x - 5}}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} + \frac{275 \sqrt{55} i \left (x + \frac{3}{5}\right )^{2} \sqrt{10 x - 5}}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} + \frac{1210 \sqrt{55} i \left (x + \frac{3}{5}\right ) \sqrt{10 x - 5}}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} - \frac{26620 \sqrt{5} \left (x + \frac{3}{5}\right )}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} - \frac{2662 \sqrt{55} i \sqrt{10 x - 5}}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} + \frac{29282 \sqrt{5}}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} & \text{for}\: \frac{10 \left |{x + \frac{3}{5}}\right |}{11} > 1 \\\frac{125 \sqrt{55} \sqrt{- 10 x + 5} \left (x + \frac{3}{5}\right )^{3}}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} + \frac{275 \sqrt{55} \sqrt{- 10 x + 5} \left (x + \frac{3}{5}\right )^{2}}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} + \frac{1210 \sqrt{55} \sqrt{- 10 x + 5} \left (x + \frac{3}{5}\right )}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} - \frac{2662 \sqrt{55} \sqrt{- 10 x + 5}}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} - \frac{26620 \sqrt{5} \left (x + \frac{3}{5}\right )}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} + \frac{29282 \sqrt{5}}{50 \sqrt{11} \left (x + \frac{3}{5}\right ) - 55 \sqrt{11}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**3/(1-2*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.221699, size = 59, normalized size = 1.11 \[ \frac{25}{8} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{275}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1815}{8} \, \sqrt{-2 \, x + 1} + \frac{1331}{8 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/(-2*x + 1)^(3/2),x, algorithm="giac")
[Out]