Optimal. Leaf size=79 \[ \frac{27}{32} (1-2 x)^{15/2}-\frac{4671}{416} (1-2 x)^{13/2}+\frac{10773}{176} (1-2 x)^{11/2}-\frac{8281}{48} (1-2 x)^{9/2}+\frac{8183}{32} (1-2 x)^{7/2}-\frac{26411}{160} (1-2 x)^{5/2} \]
[Out]
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Rubi [A] time = 0.0568757, 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 \[ \frac{27}{32} (1-2 x)^{15/2}-\frac{4671}{416} (1-2 x)^{13/2}+\frac{10773}{176} (1-2 x)^{11/2}-\frac{8281}{48} (1-2 x)^{9/2}+\frac{8183}{32} (1-2 x)^{7/2}-\frac{26411}{160} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x),x]
[Out]
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Rubi in Sympy [A] time = 9.0286, size = 70, normalized size = 0.89 \[ \frac{27 \left (- 2 x + 1\right )^{\frac{15}{2}}}{32} - \frac{4671 \left (- 2 x + 1\right )^{\frac{13}{2}}}{416} + \frac{10773 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} - \frac{8281 \left (- 2 x + 1\right )^{\frac{9}{2}}}{48} + \frac{8183 \left (- 2 x + 1\right )^{\frac{7}{2}}}{32} - \frac{26411 \left (- 2 x + 1\right )^{\frac{5}{2}}}{160} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(3/2)*(2+3*x)**4*(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0303923, size = 38, normalized size = 0.48 \[ -\frac{(1-2 x)^{5/2} \left (57915 x^5+240570 x^4+424440 x^3+410320 x^2+230000 x+66592\right )}{2145} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^4*(3 + 5*x),x]
[Out]
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Maple [A] time = 0.005, size = 35, normalized size = 0.4 \[ -{\frac{57915\,{x}^{5}+240570\,{x}^{4}+424440\,{x}^{3}+410320\,{x}^{2}+230000\,x+66592}{2145} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x),x)
[Out]
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Maxima [A] time = 1.34469, size = 74, normalized size = 0.94 \[ \frac{27}{32} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} - \frac{4671}{416} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{10773}{176} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{8281}{48} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{8183}{32} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{26411}{160} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^4*(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215723, size = 59, normalized size = 0.75 \[ -\frac{1}{2145} \,{\left (231660 \, x^{7} + 730620 \, x^{6} + 793395 \, x^{5} + 184090 \, x^{4} - 296840 \, x^{3} - 243312 \, x^{2} - 36368 \, x + 66592\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^4*(-2*x + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.47068, size = 70, normalized size = 0.89 \[ \frac{27 \left (- 2 x + 1\right )^{\frac{15}{2}}}{32} - \frac{4671 \left (- 2 x + 1\right )^{\frac{13}{2}}}{416} + \frac{10773 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} - \frac{8281 \left (- 2 x + 1\right )^{\frac{9}{2}}}{48} + \frac{8183 \left (- 2 x + 1\right )^{\frac{7}{2}}}{32} - \frac{26411 \left (- 2 x + 1\right )^{\frac{5}{2}}}{160} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(3/2)*(2+3*x)**4*(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.212437, size = 131, normalized size = 1.66 \[ -\frac{27}{32} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} - \frac{4671}{416} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{10773}{176} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{8281}{48} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{8183}{32} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{26411}{160} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^4*(-2*x + 1)^(3/2),x, algorithm="giac")
[Out]