Optimal. Leaf size=79 \[ \frac{405}{416} (1-2 x)^{13/2}-\frac{4671}{352} (1-2 x)^{11/2}+\frac{1197}{16} (1-2 x)^{9/2}-\frac{3549}{16} (1-2 x)^{7/2}+\frac{57281}{160} (1-2 x)^{5/2}-\frac{26411}{96} (1-2 x)^{3/2} \]
[Out]
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Rubi [A] time = 0.0560559, antiderivative size = 79, 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 \[ \frac{405}{416} (1-2 x)^{13/2}-\frac{4671}{352} (1-2 x)^{11/2}+\frac{1197}{16} (1-2 x)^{9/2}-\frac{3549}{16} (1-2 x)^{7/2}+\frac{57281}{160} (1-2 x)^{5/2}-\frac{26411}{96} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x),x]
[Out]
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Rubi in Sympy [A] time = 9.08667, size = 70, normalized size = 0.89 \[ \frac{405 \left (- 2 x + 1\right )^{\frac{13}{2}}}{416} - \frac{4671 \left (- 2 x + 1\right )^{\frac{11}{2}}}{352} + \frac{1197 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} - \frac{3549 \left (- 2 x + 1\right )^{\frac{7}{2}}}{16} + \frac{57281 \left (- 2 x + 1\right )^{\frac{5}{2}}}{160} - \frac{26411 \left (- 2 x + 1\right )^{\frac{3}{2}}}{96} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**4*(3+5*x)*(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0277649, size = 38, normalized size = 0.48 \[ -\frac{(1-2 x)^{3/2} \left (66825 x^5+288360 x^4+540000 x^3+577080 x^2+388704 x+163888\right )}{2145} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x),x]
[Out]
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Maple [A] time = 0.004, size = 35, normalized size = 0.4 \[ -{\frac{66825\,{x}^{5}+288360\,{x}^{4}+540000\,{x}^{3}+577080\,{x}^{2}+388704\,x+163888}{2145} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^4*(3+5*x)*(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.36371, size = 74, normalized size = 0.94 \[ \frac{405}{416} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{4671}{352} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{1197}{16} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{3549}{16} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{57281}{160} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{26411}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206573, size = 53, normalized size = 0.67 \[ \frac{1}{2145} \,{\left (133650 \, x^{6} + 509895 \, x^{5} + 791640 \, x^{4} + 614160 \, x^{3} + 200328 \, x^{2} - 60928 \, x - 163888\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.32226, size = 70, normalized size = 0.89 \[ \frac{405 \left (- 2 x + 1\right )^{\frac{13}{2}}}{416} - \frac{4671 \left (- 2 x + 1\right )^{\frac{11}{2}}}{352} + \frac{1197 \left (- 2 x + 1\right )^{\frac{9}{2}}}{16} - \frac{3549 \left (- 2 x + 1\right )^{\frac{7}{2}}}{16} + \frac{57281 \left (- 2 x + 1\right )^{\frac{5}{2}}}{160} - \frac{26411 \left (- 2 x + 1\right )^{\frac{3}{2}}}{96} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**4*(3+5*x)*(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.215343, size = 122, normalized size = 1.54 \[ \frac{405}{416} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{4671}{352} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{1197}{16} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{3549}{16} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{57281}{160} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{26411}{96} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="giac")
[Out]