Optimal. Leaf size=53 \[ \frac{5}{8} (1-2 x)^{9/2}-\frac{309}{56} (1-2 x)^{7/2}+\frac{707}{40} (1-2 x)^{5/2}-\frac{539}{24} (1-2 x)^{3/2} \]
[Out]
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Rubi [A] time = 0.0455995, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{5}{8} (1-2 x)^{9/2}-\frac{309}{56} (1-2 x)^{7/2}+\frac{707}{40} (1-2 x)^{5/2}-\frac{539}{24} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x),x]
[Out]
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Rubi in Sympy [A] time = 6.8185, size = 46, normalized size = 0.87 \[ \frac{5 \left (- 2 x + 1\right )^{\frac{9}{2}}}{8} - \frac{309 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} + \frac{707 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} - \frac{539 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2*(3+5*x)*(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0280065, size = 33, normalized size = 0.62 \[ \frac{1}{105} \sqrt{1-2 x} \left (1050 x^4+2535 x^3+2046 x^2+244 x-1016\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^2*(3 + 5*x),x]
[Out]
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Maple [A] time = 0.006, size = 25, normalized size = 0.5 \[ -{\frac{525\,{x}^{3}+1530\,{x}^{2}+1788\,x+1016}{105} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2*(3+5*x)*(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.35691, size = 50, normalized size = 0.94 \[ \frac{5}{8} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{309}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{707}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{539}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^2*sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204373, size = 39, normalized size = 0.74 \[ \frac{1}{105} \,{\left (1050 \, x^{4} + 2535 \, x^{3} + 2046 \, x^{2} + 244 \, x - 1016\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^2*sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.03171, size = 46, normalized size = 0.87 \[ \frac{5 \left (- 2 x + 1\right )^{\frac{9}{2}}}{8} - \frac{309 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} + \frac{707 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} - \frac{539 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**2*(3+5*x)*(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213263, size = 78, normalized size = 1.47 \[ \frac{5}{8} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{309}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{707}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{539}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^2*sqrt(-2*x + 1),x, algorithm="giac")
[Out]