Optimal. Leaf size=92 \[ -\frac{135}{64} (1-2 x)^{15/2}+\frac{13905}{416} (1-2 x)^{13/2}-\frac{159111}{704} (1-2 x)^{11/2}+\frac{40453}{48} (1-2 x)^{9/2}-\frac{118993}{64} (1-2 x)^{7/2}+\frac{381073}{160} (1-2 x)^{5/2}-\frac{290521}{192} (1-2 x)^{3/2} \]
[Out]
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Rubi [A] time = 0.0684216, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ -\frac{135}{64} (1-2 x)^{15/2}+\frac{13905}{416} (1-2 x)^{13/2}-\frac{159111}{704} (1-2 x)^{11/2}+\frac{40453}{48} (1-2 x)^{9/2}-\frac{118993}{64} (1-2 x)^{7/2}+\frac{381073}{160} (1-2 x)^{5/2}-\frac{290521}{192} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 10.3154, size = 82, normalized size = 0.89 \[ - \frac{135 \left (- 2 x + 1\right )^{\frac{15}{2}}}{64} + \frac{13905 \left (- 2 x + 1\right )^{\frac{13}{2}}}{416} - \frac{159111 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{40453 \left (- 2 x + 1\right )^{\frac{9}{2}}}{48} - \frac{118993 \left (- 2 x + 1\right )^{\frac{7}{2}}}{64} + \frac{381073 \left (- 2 x + 1\right )^{\frac{5}{2}}}{160} - \frac{290521 \left (- 2 x + 1\right )^{\frac{3}{2}}}{192} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**4*(3+5*x)**2*(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0593655, size = 43, normalized size = 0.47 \[ -\frac{(1-2 x)^{3/2} \left (289575 x^6+1425600 x^5+3106755 x^4+3960500 x^3+3298140 x^2+1895832 x+734904\right )}{2145} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{289575\,{x}^{6}+1425600\,{x}^{5}+3106755\,{x}^{4}+3960500\,{x}^{3}+3298140\,{x}^{2}+1895832\,x+734904}{2145} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^4*(3+5*x)^2*(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.34927, size = 86, normalized size = 0.93 \[ -\frac{135}{64} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{13905}{416} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{159111}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{40453}{48} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{118993}{64} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{381073}{160} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{290521}{192} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206349, size = 59, normalized size = 0.64 \[ \frac{1}{2145} \,{\left (579150 \, x^{7} + 2561625 \, x^{6} + 4787910 \, x^{5} + 4814245 \, x^{4} + 2635780 \, x^{3} + 493524 \, x^{2} - 426024 \, x - 734904\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.36127, size = 82, normalized size = 0.89 \[ - \frac{135 \left (- 2 x + 1\right )^{\frac{15}{2}}}{64} + \frac{13905 \left (- 2 x + 1\right )^{\frac{13}{2}}}{416} - \frac{159111 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{40453 \left (- 2 x + 1\right )^{\frac{9}{2}}}{48} - \frac{118993 \left (- 2 x + 1\right )^{\frac{7}{2}}}{64} + \frac{381073 \left (- 2 x + 1\right )^{\frac{5}{2}}}{160} - \frac{290521 \left (- 2 x + 1\right )^{\frac{3}{2}}}{192} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**4*(3+5*x)**2*(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.216021, size = 143, normalized size = 1.55 \[ \frac{135}{64} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{13905}{416} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{159111}{704} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{40453}{48} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{118993}{64} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{381073}{160} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{290521}{192} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(3*x + 2)^4*sqrt(-2*x + 1),x, algorithm="giac")
[Out]