Optimal. Leaf size=105 \[ -\frac{27 (2 x+3)^{11/2}}{1408}+\frac{63}{128} (2 x+3)^{9/2}-\frac{3519}{896} (2 x+3)^{7/2}+\frac{2095}{128} (2 x+3)^{5/2}-\frac{17201}{384} (2 x+3)^{3/2}+\frac{16005}{128} \sqrt{2 x+3}+\frac{7925}{128 \sqrt{2 x+3}}-\frac{1625}{384 (2 x+3)^{3/2}} \]
[Out]
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Rubi [A] time = 0.0867551, 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 \[ -\frac{27 (2 x+3)^{11/2}}{1408}+\frac{63}{128} (2 x+3)^{9/2}-\frac{3519}{896} (2 x+3)^{7/2}+\frac{2095}{128} (2 x+3)^{5/2}-\frac{17201}{384} (2 x+3)^{3/2}+\frac{16005}{128} \sqrt{2 x+3}+\frac{7925}{128 \sqrt{2 x+3}}-\frac{1625}{384 (2 x+3)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[((5 - x)*(2 + 5*x + 3*x^2)^3)/(3 + 2*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 15.6552, size = 94, normalized size = 0.9 \[ - \frac{27 \left (2 x + 3\right )^{\frac{11}{2}}}{1408} + \frac{63 \left (2 x + 3\right )^{\frac{9}{2}}}{128} - \frac{3519 \left (2 x + 3\right )^{\frac{7}{2}}}{896} + \frac{2095 \left (2 x + 3\right )^{\frac{5}{2}}}{128} - \frac{17201 \left (2 x + 3\right )^{\frac{3}{2}}}{384} + \frac{16005 \sqrt{2 x + 3}}{128} + \frac{7925}{128 \sqrt{2 x + 3}} - \frac{1625}{384 \left (2 x + 3\right )^{\frac{3}{2}}} \]
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)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0443695, size = 48, normalized size = 0.46 \[ -\frac{567 x^7-1323 x^6-9666 x^5-21360 x^4-17663 x^3-42003 x^2-184566 x-181486}{231 (2 x+3)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((5 - x)*(2 + 5*x + 3*x^2)^3)/(3 + 2*x)^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 45, normalized size = 0.4 \[ -{\frac{567\,{x}^{7}-1323\,{x}^{6}-9666\,{x}^{5}-21360\,{x}^{4}-17663\,{x}^{3}-42003\,{x}^{2}-184566\,x-181486}{231} \left ( 3+2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3*x^2+5*x+2)^3/(3+2*x)^(5/2),x)
[Out]
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Maxima [A] time = 0.707979, size = 93, normalized size = 0.89 \[ -\frac{27}{1408} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{63}{128} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} - \frac{3519}{896} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{2095}{128} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} - \frac{17201}{384} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} + \frac{16005}{128} \, \sqrt{2 \, x + 3} + \frac{25 \,{\left (951 \, x + 1394\right )}}{192 \,{\left (2 \, x + 3\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^3*(x - 5)/(2*x + 3)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.273172, size = 59, normalized size = 0.56 \[ -\frac{567 \, x^{7} - 1323 \, x^{6} - 9666 \, x^{5} - 21360 \, x^{4} - 17663 \, x^{3} - 42003 \, x^{2} - 184566 \, x - 181486}{231 \,{\left (2 \, x + 3\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^3*(x - 5)/(2*x + 3)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \int \left (- \frac{292 x}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right )\, dx - \int \left (- \frac{870 x^{2}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right )\, dx - \int \left (- \frac{1339 x^{3}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right )\, dx - \int \left (- \frac{1090 x^{4}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right )\, dx - \int \left (- \frac{396 x^{5}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right )\, dx - \int \frac{27 x^{7}}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\, dx - \int \left (- \frac{40}{4 x^{2} \sqrt{2 x + 3} + 12 x \sqrt{2 x + 3} + 9 \sqrt{2 x + 3}}\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)*(3*x**2+5*x+2)**3/(3+2*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.272708, size = 93, normalized size = 0.89 \[ -\frac{27}{1408} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{63}{128} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} - \frac{3519}{896} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{2095}{128} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} - \frac{17201}{384} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} + \frac{16005}{128} \, \sqrt{2 \, x + 3} + \frac{25 \,{\left (951 \, x + 1394\right )}}{192 \,{\left (2 \, x + 3\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^3*(x - 5)/(2*x + 3)^(5/2),x, algorithm="giac")
[Out]