Optimal. Leaf size=105 \[ \frac{3645 (1-2 x)^{19/2}}{2432}-\frac{59049 (1-2 x)^{17/2}}{2176}+\frac{136647}{640} (1-2 x)^{15/2}-\frac{1580985 (1-2 x)^{13/2}}{1664}+\frac{3658095 (1-2 x)^{11/2}}{1408}-\frac{564235}{128} (1-2 x)^{9/2}+\frac{559433}{128} (1-2 x)^{7/2}-\frac{1294139}{640} (1-2 x)^{5/2} \]
[Out]
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Rubi [A] time = 0.0678274, 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 \[ \frac{3645 (1-2 x)^{19/2}}{2432}-\frac{59049 (1-2 x)^{17/2}}{2176}+\frac{136647}{640} (1-2 x)^{15/2}-\frac{1580985 (1-2 x)^{13/2}}{1664}+\frac{3658095 (1-2 x)^{11/2}}{1408}-\frac{564235}{128} (1-2 x)^{9/2}+\frac{559433}{128} (1-2 x)^{7/2}-\frac{1294139}{640} (1-2 x)^{5/2} \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^(3/2)*(2 + 3*x)^6*(3 + 5*x),x]
[Out]
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Rubi in Sympy [A] time = 11.2754, size = 94, normalized size = 0.9 \[ \frac{3645 \left (- 2 x + 1\right )^{\frac{19}{2}}}{2432} - \frac{59049 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} + \frac{136647 \left (- 2 x + 1\right )^{\frac{15}{2}}}{640} - \frac{1580985 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} + \frac{3658095 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} - \frac{564235 \left (- 2 x + 1\right )^{\frac{9}{2}}}{128} + \frac{559433 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} - \frac{1294139 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(3/2)*(2+3*x)**6*(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0364784, size = 48, normalized size = 0.46 \[ -\frac{(1-2 x)^{5/2} \left (44304975 x^7+246022920 x^6+607227192 x^5+876286620 x^4+817490880 x^3+512679760 x^2+214047840 x+51677856\right )}{230945} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^6*(3 + 5*x),x]
[Out]
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Maple [A] time = 0.004, size = 45, normalized size = 0.4 \[ -{\frac{44304975\,{x}^{7}+246022920\,{x}^{6}+607227192\,{x}^{5}+876286620\,{x}^{4}+817490880\,{x}^{3}+512679760\,{x}^{2}+214047840\,x+51677856}{230945} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(3/2)*(2+3*x)^6*(3+5*x),x)
[Out]
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Maxima [A] time = 1.37242, size = 99, normalized size = 0.94 \[ \frac{3645}{2432} \,{\left (-2 \, x + 1\right )}^{\frac{19}{2}} - \frac{59049}{2176} \,{\left (-2 \, x + 1\right )}^{\frac{17}{2}} + \frac{136647}{640} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} - \frac{1580985}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{3658095}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{564235}{128} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{559433}{128} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{1294139}{640} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)*(3*x + 2)^6*(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206947, size = 73, normalized size = 0.7 \[ -\frac{1}{230945} \,{\left (177219900 \, x^{9} + 806871780 \, x^{8} + 1489122063 \, x^{7} + 1322260632 \, x^{6} + 372044232 \, x^{5} - 342957860 \, x^{4} - 377036800 \, x^{3} - 136800176 \, x^{2} + 7336416 \, x + 51677856\right )} \sqrt{-2 \, x + 1} \]
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 [A] time = 10.0804, size = 94, normalized size = 0.9 \[ \frac{3645 \left (- 2 x + 1\right )^{\frac{19}{2}}}{2432} - \frac{59049 \left (- 2 x + 1\right )^{\frac{17}{2}}}{2176} + \frac{136647 \left (- 2 x + 1\right )^{\frac{15}{2}}}{640} - \frac{1580985 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} + \frac{3658095 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} - \frac{564235 \left (- 2 x + 1\right )^{\frac{9}{2}}}{128} + \frac{559433 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} - \frac{1294139 \left (- 2 x + 1\right )^{\frac{5}{2}}}{640} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(3/2)*(2+3*x)**6*(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.226311, size = 1, normalized size = 0.01 \[ \mathit{Done} \]
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]