Optimal. Leaf size=105 \[ \frac{3645 (1-2 x)^{17/2}}{2176}-\frac{19683}{640} (1-2 x)^{15/2}+\frac{409941 (1-2 x)^{13/2}}{1664}-\frac{1580985 (1-2 x)^{11/2}}{1408}+\frac{406455}{128} (1-2 x)^{9/2}-\frac{725445}{128} (1-2 x)^{7/2}+\frac{3916031}{640} (1-2 x)^{5/2}-\frac{1294139}{384} (1-2 x)^{3/2} \]
[Out]
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Rubi [A] time = 0.0662704, 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 \[ \frac{3645 (1-2 x)^{17/2}}{2176}-\frac{19683}{640} (1-2 x)^{15/2}+\frac{409941 (1-2 x)^{13/2}}{1664}-\frac{1580985 (1-2 x)^{11/2}}{1408}+\frac{406455}{128} (1-2 x)^{9/2}-\frac{725445}{128} (1-2 x)^{7/2}+\frac{3916031}{640} (1-2 x)^{5/2}-\frac{1294139}{384} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]*(2 + 3*x)^6*(3 + 5*x),x]
[Out]
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Rubi in Sympy [A] time = 10.9717, size = 94, normalized size = 0.9 \[ \frac{3645 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} - \frac{19683 \left (- 2 x + 1\right )^{\frac{15}{2}}}{640} + \frac{409941 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} - \frac{1580985 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} + \frac{406455 \left (- 2 x + 1\right )^{\frac{9}{2}}}{128} - \frac{725445 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} + \frac{3916031 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} - \frac{1294139 \left (- 2 x + 1\right )^{\frac{3}{2}}}{384} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**6*(3+5*x)*(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0358343, size = 48, normalized size = 0.46 \[ -\frac{(1-2 x)^{3/2} \left (7818525 x^7+44409222 x^6+113196204 x^5+171389520 x^4+172440720 x^3+122662080 x^2+64000896 x+23667392\right )}{36465} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^6*(3 + 5*x),x]
[Out]
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Maple [A] time = 0.006, size = 45, normalized size = 0.4 \[ -{\frac{7818525\,{x}^{7}+44409222\,{x}^{6}+113196204\,{x}^{5}+171389520\,{x}^{4}+172440720\,{x}^{3}+122662080\,{x}^{2}+64000896\,x+23667392}{36465} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^6*(3+5*x)*(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.3447, size = 99, normalized size = 0.94 \[ \frac{3645}{2176} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} - \frac{19683}{640} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{409941}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{1580985}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{406455}{128} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{725445}{128} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{3916031}{640} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{1294139}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^6*sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206321, size = 66, normalized size = 0.63 \[ \frac{1}{36465} \,{\left (15637050 \, x^{8} + 80999919 \, x^{7} + 181983186 \, x^{6} + 229582836 \, x^{5} + 173491920 \, x^{4} + 72883440 \, x^{3} + 5339712 \, x^{2} - 16666112 \, x - 23667392\right )} \sqrt{-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^6*sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.90783, size = 94, normalized size = 0.9 \[ \frac{3645 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} - \frac{19683 \left (- 2 x + 1\right )^{\frac{15}{2}}}{640} + \frac{409941 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} - \frac{1580985 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} + \frac{406455 \left (- 2 x + 1\right )^{\frac{9}{2}}}{128} - \frac{725445 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} + \frac{3916031 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} - \frac{1294139 \left (- 2 x + 1\right )^{\frac{3}{2}}}{384} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**6*(3+5*x)*(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.217735, size = 165, normalized size = 1.57 \[ \frac{3645}{2176} \,{\left (2 \, x - 1\right )}^{8} \sqrt{-2 \, x + 1} + \frac{19683}{640} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{409941}{1664} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{1580985}{1408} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{406455}{128} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{725445}{128} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{3916031}{640} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{1294139}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^6*sqrt(-2*x + 1),x, algorithm="giac")
[Out]