Optimal. Leaf size=40 \[ -\frac{5}{4} (1-2 x)^{5/2}+\frac{55}{6} (1-2 x)^{3/2}-\frac{121}{4} \sqrt{1-2 x} \]
[Out]
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Rubi [A] time = 0.0289431, antiderivative size = 40, 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 \[ -\frac{5}{4} (1-2 x)^{5/2}+\frac{55}{6} (1-2 x)^{3/2}-\frac{121}{4} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 5.15926, size = 34, normalized size = 0.85 \[ - \frac{5 \left (- 2 x + 1\right )^{\frac{5}{2}}}{4} + \frac{55 \left (- 2 x + 1\right )^{\frac{3}{2}}}{6} - \frac{121 \sqrt{- 2 x + 1}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0207163, size = 23, normalized size = 0.57 \[ -\frac{1}{3} \sqrt{1-2 x} \left (15 x^2+40 x+67\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.004, size = 20, normalized size = 0.5 \[ -{\frac{15\,{x}^{2}+40\,x+67}{3}\sqrt{1-2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.34789, size = 38, normalized size = 0.95 \[ -\frac{5}{4} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{55}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{121}{4} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213117, size = 26, normalized size = 0.65 \[ -\frac{1}{3} \,{\left (15 \, x^{2} + 40 \, x + 67\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.1714, size = 134, normalized size = 3.35 \[ \begin{cases} - \sqrt{5} i \left (x + \frac{3}{5}\right )^{2} \sqrt{10 x - 5} - \frac{22 \sqrt{5} i \left (x + \frac{3}{5}\right ) \sqrt{10 x - 5}}{15} - \frac{242 \sqrt{5} i \sqrt{10 x - 5}}{75} & \text{for}\: \frac{10 \left |{x + \frac{3}{5}}\right |}{11} > 1 \\- \sqrt{5} \sqrt{- 10 x + 5} \left (x + \frac{3}{5}\right )^{2} - \frac{22 \sqrt{5} \sqrt{- 10 x + 5} \left (x + \frac{3}{5}\right )}{15} - \frac{242 \sqrt{5} \sqrt{- 10 x + 5}}{75} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3+5*x)**2/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.209799, size = 47, normalized size = 1.18 \[ -\frac{5}{4} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{55}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{121}{4} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/sqrt(-2*x + 1),x, algorithm="giac")
[Out]