Optimal. Leaf size=105 \[ \frac{3645 (1-2 x)^{13/2}}{1664}-\frac{59049 (1-2 x)^{11/2}}{1408}+\frac{45549}{128} (1-2 x)^{9/2}-\frac{225855}{128} (1-2 x)^{7/2}+\frac{731619}{128} (1-2 x)^{5/2}-\frac{1692705}{128} (1-2 x)^{3/2}+\frac{3916031}{128} \sqrt{1-2 x}+\frac{1294139}{128 \sqrt{1-2 x}} \]
[Out]
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Rubi [A] time = 0.0771053, antiderivative size = 105, 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 \[ \frac{3645 (1-2 x)^{13/2}}{1664}-\frac{59049 (1-2 x)^{11/2}}{1408}+\frac{45549}{128} (1-2 x)^{9/2}-\frac{225855}{128} (1-2 x)^{7/2}+\frac{731619}{128} (1-2 x)^{5/2}-\frac{1692705}{128} (1-2 x)^{3/2}+\frac{3916031}{128} \sqrt{1-2 x}+\frac{1294139}{128 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 11.1194, size = 94, normalized size = 0.9 \[ \frac{3645 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} - \frac{59049 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} + \frac{45549 \left (- 2 x + 1\right )^{\frac{9}{2}}}{128} - \frac{225855 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} + \frac{731619 \left (- 2 x + 1\right )^{\frac{5}{2}}}{128} - \frac{1692705 \left (- 2 x + 1\right )^{\frac{3}{2}}}{128} + \frac{3916031 \sqrt{- 2 x + 1}}{128} + \frac{1294139}{128 \sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**6*(3+5*x)/(1-2*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.032668, size = 48, normalized size = 0.46 \[ \frac{-40095 x^7-243486 x^6-687420 x^5-1230120 x^4-1663632 x^3-2109792 x^2-4512448 x+4539904}{143 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^6*(3 + 5*x))/(1 - 2*x)^(3/2),x]
[Out]
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Maple [A] time = 0.004, size = 45, normalized size = 0.4 \[ -{\frac{40095\,{x}^{7}+243486\,{x}^{6}+687420\,{x}^{5}+1230120\,{x}^{4}+1663632\,{x}^{3}+2109792\,{x}^{2}+4512448\,x-4539904}{143}{\frac{1}{\sqrt{1-2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^6*(3+5*x)/(1-2*x)^(3/2),x)
[Out]
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Maxima [A] time = 1.35339, size = 99, normalized size = 0.94 \[ \frac{3645}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{59049}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{45549}{128} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{225855}{128} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{731619}{128} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{1692705}{128} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{3916031}{128} \, \sqrt{-2 \, x + 1} + \frac{1294139}{128 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^6/(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.240006, size = 59, normalized size = 0.56 \[ -\frac{40095 \, x^{7} + 243486 \, x^{6} + 687420 \, x^{5} + 1230120 \, x^{4} + 1663632 \, x^{3} + 2109792 \, x^{2} + 4512448 \, x - 4539904}{143 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^6/(-2*x + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{6} \left (5 x + 3\right )}{\left (- 2 x + 1\right )^{\frac{3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**6*(3+5*x)/(1-2*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212199, size = 146, normalized size = 1.39 \[ \frac{3645}{1664} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{59049}{1408} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{45549}{128} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{225855}{128} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{731619}{128} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{1692705}{128} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{3916031}{128} \, \sqrt{-2 \, x + 1} + \frac{1294139}{128 \, \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^6/(-2*x + 1)^(3/2),x, algorithm="giac")
[Out]