Optimal. Leaf size=22 \[ \frac{2 \sqrt{5 x+3}}{11 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.0162011, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ \frac{2 \sqrt{5 x+3}}{11 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]
[Out]
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Rubi in Sympy [A] time = 2.86661, size = 19, normalized size = 0.86 \[ \frac{2 \sqrt{5 x + 3}}{11 \sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**(3/2)/(3+5*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0210821, size = 22, normalized size = 1. \[ \frac{2 \sqrt{5 x+3}}{11 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]
[Out]
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Maple [A] time = 0.006, size = 17, normalized size = 0.8 \[{\frac{2}{11}\sqrt{3+5\,x}{\frac{1}{\sqrt{1-2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^(3/2)/(3+5*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.48024, size = 28, normalized size = 1.27 \[ -\frac{2 \, \sqrt{-10 \, x^{2} - x + 3}}{11 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x + 3)*(-2*x + 1)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221591, size = 31, normalized size = 1.41 \[ -\frac{2 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{11 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x + 3)*(-2*x + 1)^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.92408, size = 49, normalized size = 2.23 \[ \begin{cases} \frac{\sqrt{10}}{11 \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}}} & \text{for}\: \frac{11 \left |{\frac{1}{x + \frac{3}{5}}}\right |}{10} > 1 \\- \frac{\sqrt{10} i}{11 \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**(3/2)/(3+5*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.223246, size = 35, normalized size = 1.59 \[ -\frac{2 \, \sqrt{5} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{55 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x + 3)*(-2*x + 1)^(3/2)),x, algorithm="giac")
[Out]