Optimal. Leaf size=38 \[ -\frac{15}{4} \sqrt{1-2 x}-\frac{17}{\sqrt{1-2 x}}+\frac{77}{12 (1-2 x)^{3/2}} \]
[Out]
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Rubi [A] time = 0.0399739, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{15}{4} \sqrt{1-2 x}-\frac{17}{\sqrt{1-2 x}}+\frac{77}{12 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 5.82606, size = 32, normalized size = 0.84 \[ - \frac{15 \sqrt{- 2 x + 1}}{4} - \frac{17}{\sqrt{- 2 x + 1}} + \frac{77}{12 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)*(3+5*x)/(1-2*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0111421, size = 23, normalized size = 0.61 \[ -\frac{45 x^2-147 x+43}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)*(3 + 5*x))/(1 - 2*x)^(5/2),x]
[Out]
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Maple [A] time = 0.003, size = 20, normalized size = 0.5 \[ -{\frac{45\,{x}^{2}-147\,x+43}{3} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)*(3+5*x)/(1-2*x)^(5/2),x)
[Out]
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Maxima [A] time = 1.33948, size = 32, normalized size = 0.84 \[ -\frac{15}{4} \, \sqrt{-2 \, x + 1} + \frac{408 \, x - 127}{12 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)/(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.211577, size = 35, normalized size = 0.92 \[ \frac{45 \, x^{2} - 147 \, x + 43}{3 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)/(-2*x + 1)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.13503, size = 75, normalized size = 1.97 \[ \frac{45 x^{2}}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} - \frac{147 x}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} + \frac{43}{6 x \sqrt{- 2 x + 1} - 3 \sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)*(3+5*x)/(1-2*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.208689, size = 42, normalized size = 1.11 \[ -\frac{15}{4} \, \sqrt{-2 \, x + 1} - \frac{408 \, x - 127}{12 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)/(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]