Optimal. Leaf size=45 \[ \frac{7 \sqrt{5 x+3}}{33 (1-2 x)^{3/2}}-\frac{29 \sqrt{5 x+3}}{363 \sqrt{1-2 x}} \]
[Out]
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Rubi [A] time = 0.046817, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{7 \sqrt{5 x+3}}{33 (1-2 x)^{3/2}}-\frac{29 \sqrt{5 x+3}}{363 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]
[Out]
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Rubi in Sympy [A] time = 5.12597, size = 39, normalized size = 0.87 \[ - \frac{29 \sqrt{5 x + 3}}{363 \sqrt{- 2 x + 1}} + \frac{7 \sqrt{5 x + 3}}{33 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)/(1-2*x)**(5/2)/(3+5*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.037447, size = 27, normalized size = 0.6 \[ \frac{2 \sqrt{5 x+3} (29 x+24)}{363 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)/((1 - 2*x)^(5/2)*Sqrt[3 + 5*x]),x]
[Out]
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Maple [A] time = 0.004, size = 22, normalized size = 0.5 \[{\frac{58\,x+48}{363}\sqrt{3+5\,x} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)/(1-2*x)^(5/2)/(3+5*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.49072, size = 65, normalized size = 1.44 \[ \frac{7 \, \sqrt{-10 \, x^{2} - x + 3}}{33 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{29 \, \sqrt{-10 \, x^{2} - x + 3}}{363 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)/(sqrt(5*x + 3)*(-2*x + 1)^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21652, size = 45, normalized size = 1. \[ \frac{2 \,{\left (29 \, x + 24\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{363 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)/(sqrt(5*x + 3)*(-2*x + 1)^(5/2)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{3 x + 2}{\left (- 2 x + 1\right )^{\frac{5}{2}} \sqrt{5 x + 3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)/(1-2*x)**(5/2)/(3+5*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.251923, size = 53, normalized size = 1.18 \[ \frac{2 \,{\left (29 \, \sqrt{5}{\left (5 \, x + 3\right )} + 33 \, \sqrt{5}\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{9075 \,{\left (2 \, x - 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)/(sqrt(5*x + 3)*(-2*x + 1)^(5/2)),x, algorithm="giac")
[Out]