Optimal. Leaf size=66 \[ -\frac{15}{16} (1-2 x)^{9/2}+\frac{621}{56} (1-2 x)^{7/2}-\frac{1071}{20} (1-2 x)^{5/2}+\frac{3283}{24} (1-2 x)^{3/2}-\frac{3773}{16} \sqrt{1-2 x} \]
[Out]
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Rubi [A] time = 0.0549475, antiderivative size = 66, 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 \[ -\frac{15}{16} (1-2 x)^{9/2}+\frac{621}{56} (1-2 x)^{7/2}-\frac{1071}{20} (1-2 x)^{5/2}+\frac{3283}{24} (1-2 x)^{3/2}-\frac{3773}{16} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^3*(3 + 5*x))/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 7.85605, size = 58, normalized size = 0.88 \[ - \frac{15 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} + \frac{621 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{1071 \left (- 2 x + 1\right )^{\frac{5}{2}}}{20} + \frac{3283 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{3773 \sqrt{- 2 x + 1}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3*(3+5*x)/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.03255, size = 33, normalized size = 0.5 \[ -\frac{1}{105} \sqrt{1-2 x} \left (1575 x^4+6165 x^3+10881 x^2+12434 x+14954\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^3*(3 + 5*x))/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.005, size = 30, normalized size = 0.5 \[ -{\frac{1575\,{x}^{4}+6165\,{x}^{3}+10881\,{x}^{2}+12434\,x+14954}{105}\sqrt{1-2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3*(3+5*x)/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.34887, size = 62, normalized size = 0.94 \[ -\frac{15}{16} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{621}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{1071}{20} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{3283}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{3773}{16} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209404, size = 39, normalized size = 0.59 \[ -\frac{1}{105} \,{\left (1575 \, x^{4} + 6165 \, x^{3} + 10881 \, x^{2} + 12434 \, x + 14954\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 9.9098, size = 58, normalized size = 0.88 \[ - \frac{15 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} + \frac{621 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{1071 \left (- 2 x + 1\right )^{\frac{5}{2}}}{20} + \frac{3283 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{3773 \sqrt{- 2 x + 1}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3*(3+5*x)/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.20752, size = 90, normalized size = 1.36 \[ -\frac{15}{16} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{621}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{1071}{20} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{3283}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{3773}{16} \, \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="giac")
[Out]