Optimal. Leaf size=105 \[ -\frac{27 (2 x+3)^{13/2}}{1664}+\frac{567 (2 x+3)^{11/2}}{1408}-\frac{391}{128} (2 x+3)^{9/2}+\frac{10475}{896} (2 x+3)^{7/2}-\frac{17201}{640} (2 x+3)^{5/2}+\frac{5335}{128} (2 x+3)^{3/2}-\frac{7925}{128} \sqrt{2 x+3}-\frac{1625}{128 \sqrt{2 x+3}} \]
[Out]
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Rubi [A] time = 0.0885867, antiderivative size = 105, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.037 \[ -\frac{27 (2 x+3)^{13/2}}{1664}+\frac{567 (2 x+3)^{11/2}}{1408}-\frac{391}{128} (2 x+3)^{9/2}+\frac{10475}{896} (2 x+3)^{7/2}-\frac{17201}{640} (2 x+3)^{5/2}+\frac{5335}{128} (2 x+3)^{3/2}-\frac{7925}{128} \sqrt{2 x+3}-\frac{1625}{128 \sqrt{2 x+3}} \]
Antiderivative was successfully verified.
[In] Int[((5 - x)*(2 + 5*x + 3*x^2)^3)/(3 + 2*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 15.7985, size = 94, normalized size = 0.9 \[ - \frac{27 \left (2 x + 3\right )^{\frac{13}{2}}}{1664} + \frac{567 \left (2 x + 3\right )^{\frac{11}{2}}}{1408} - \frac{391 \left (2 x + 3\right )^{\frac{9}{2}}}{128} + \frac{10475 \left (2 x + 3\right )^{\frac{7}{2}}}{896} - \frac{17201 \left (2 x + 3\right )^{\frac{5}{2}}}{640} + \frac{5335 \left (2 x + 3\right )^{\frac{3}{2}}}{128} - \frac{7925 \sqrt{2 x + 3}}{128} - \frac{1625}{128 \sqrt{2 x + 3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)*(3*x**2+5*x+2)**3/(3+2*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0422781, size = 48, normalized size = 0.46 \[ -\frac{10395 x^7-19845 x^6-180530 x^5-392500 x^4-398339 x^3-256433 x^2+77138 x+431614}{5005 \sqrt{2 x+3}} \]
Antiderivative was successfully verified.
[In] Integrate[((5 - x)*(2 + 5*x + 3*x^2)^3)/(3 + 2*x)^(3/2),x]
[Out]
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Maple [A] time = 0.007, size = 45, normalized size = 0.4 \[ -{\frac{10395\,{x}^{7}-19845\,{x}^{6}-180530\,{x}^{5}-392500\,{x}^{4}-398339\,{x}^{3}-256433\,{x}^{2}+77138\,x+431614}{5005}{\frac{1}{\sqrt{3+2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3*x^2+5*x+2)^3/(3+2*x)^(3/2),x)
[Out]
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Maxima [A] time = 0.70663, size = 99, normalized size = 0.94 \[ -\frac{27}{1664} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} + \frac{567}{1408} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} - \frac{391}{128} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} + \frac{10475}{896} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} - \frac{17201}{640} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} + \frac{5335}{128} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} - \frac{7925}{128} \, \sqrt{2 \, x + 3} - \frac{1625}{128 \, \sqrt{2 \, x + 3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^3*(x - 5)/(2*x + 3)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.280273, size = 59, normalized size = 0.56 \[ -\frac{10395 \, x^{7} - 19845 \, x^{6} - 180530 \, x^{5} - 392500 \, x^{4} - 398339 \, x^{3} - 256433 \, x^{2} + 77138 \, x + 431614}{5005 \, \sqrt{2 \, x + 3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^3*(x - 5)/(2*x + 3)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \int \left (- \frac{292 x}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right )\, dx - \int \left (- \frac{870 x^{2}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right )\, dx - \int \left (- \frac{1339 x^{3}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right )\, dx - \int \left (- \frac{1090 x^{4}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right )\, dx - \int \left (- \frac{396 x^{5}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right )\, dx - \int \frac{27 x^{7}}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\, dx - \int \left (- \frac{40}{2 x \sqrt{2 x + 3} + 3 \sqrt{2 x + 3}}\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)*(3*x**2+5*x+2)**3/(3+2*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.268456, size = 99, normalized size = 0.94 \[ -\frac{27}{1664} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} + \frac{567}{1408} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} - \frac{391}{128} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} + \frac{10475}{896} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} - \frac{17201}{640} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} + \frac{5335}{128} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} - \frac{7925}{128} \, \sqrt{2 \, x + 3} - \frac{1625}{128 \, \sqrt{2 \, x + 3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^3*(x - 5)/(2*x + 3)^(3/2),x, algorithm="giac")
[Out]