Optimal. Leaf size=105 \[ -\frac{27 (2 x+3)^{19/2}}{2432}+\frac{567 (2 x+3)^{17/2}}{2176}-\frac{1173}{640} (2 x+3)^{15/2}+\frac{10475 (2 x+3)^{13/2}}{1664}-\frac{17201 (2 x+3)^{11/2}}{1408}+\frac{5335}{384} (2 x+3)^{9/2}-\frac{7925}{896} (2 x+3)^{7/2}+\frac{325}{128} (2 x+3)^{5/2} \]
[Out]
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Rubi [A] time = 0.0807269, 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 \[ -\frac{27 (2 x+3)^{19/2}}{2432}+\frac{567 (2 x+3)^{17/2}}{2176}-\frac{1173}{640} (2 x+3)^{15/2}+\frac{10475 (2 x+3)^{13/2}}{1664}-\frac{17201 (2 x+3)^{11/2}}{1408}+\frac{5335}{384} (2 x+3)^{9/2}-\frac{7925}{896} (2 x+3)^{7/2}+\frac{325}{128} (2 x+3)^{5/2} \]
Antiderivative was successfully verified.
[In] Int[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 16.1805, size = 94, normalized size = 0.9 \[ - \frac{27 \left (2 x + 3\right )^{\frac{19}{2}}}{2432} + \frac{567 \left (2 x + 3\right )^{\frac{17}{2}}}{2176} - \frac{1173 \left (2 x + 3\right )^{\frac{15}{2}}}{640} + \frac{10475 \left (2 x + 3\right )^{\frac{13}{2}}}{1664} - \frac{17201 \left (2 x + 3\right )^{\frac{11}{2}}}{1408} + \frac{5335 \left (2 x + 3\right )^{\frac{9}{2}}}{384} - \frac{7925 \left (2 x + 3\right )^{\frac{7}{2}}}{896} + \frac{325 \left (2 x + 3\right )^{\frac{5}{2}}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)*(3+2*x)**(3/2)*(3*x**2+5*x+2)**3,x)
[Out]
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Mathematica [A] time = 0.0391192, size = 48, normalized size = 0.46 \[ -\frac{(2 x+3)^{5/2} \left (6891885 x^7-8513505 x^6-117819702 x^5-270695040 x^4-295054725 x^3-173763625 x^2-53367570 x-6778218\right )}{4849845} \]
Antiderivative was successfully verified.
[In] Integrate[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^3,x]
[Out]
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Maple [A] time = 0.006, size = 45, normalized size = 0.4 \[ -{\frac{6891885\,{x}^{7}-8513505\,{x}^{6}-117819702\,{x}^{5}-270695040\,{x}^{4}-295054725\,{x}^{3}-173763625\,{x}^{2}-53367570\,x-6778218}{4849845} \left ( 3+2\,x \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3+2*x)^(3/2)*(3*x^2+5*x+2)^3,x)
[Out]
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Maxima [A] time = 0.707375, size = 99, normalized size = 0.94 \[ -\frac{27}{2432} \,{\left (2 \, x + 3\right )}^{\frac{19}{2}} + \frac{567}{2176} \,{\left (2 \, x + 3\right )}^{\frac{17}{2}} - \frac{1173}{640} \,{\left (2 \, x + 3\right )}^{\frac{15}{2}} + \frac{10475}{1664} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} - \frac{17201}{1408} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{5335}{384} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} - \frac{7925}{896} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{325}{128} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^3*(2*x + 3)^(3/2)*(x - 5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.273071, size = 73, normalized size = 0.7 \[ -\frac{1}{4849845} \,{\left (27567540 \, x^{9} + 48648600 \, x^{8} - 511413903 \, x^{7} - 2573238129 \, x^{6} - 5488936698 \, x^{5} - 6671966560 \, x^{4} - 4954126305 \, x^{3} - 2231396337 \, x^{2} - 561646746 \, x - 61003962\right )} \sqrt{2 \, x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^3*(2*x + 3)^(3/2)*(x - 5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 12.5498, size = 94, normalized size = 0.9 \[ - \frac{27 \left (2 x + 3\right )^{\frac{19}{2}}}{2432} + \frac{567 \left (2 x + 3\right )^{\frac{17}{2}}}{2176} - \frac{1173 \left (2 x + 3\right )^{\frac{15}{2}}}{640} + \frac{10475 \left (2 x + 3\right )^{\frac{13}{2}}}{1664} - \frac{17201 \left (2 x + 3\right )^{\frac{11}{2}}}{1408} + \frac{5335 \left (2 x + 3\right )^{\frac{9}{2}}}{384} - \frac{7925 \left (2 x + 3\right )^{\frac{7}{2}}}{896} + \frac{325 \left (2 x + 3\right )^{\frac{5}{2}}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)*(3+2*x)**(3/2)*(3*x**2+5*x+2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.270809, size = 99, normalized size = 0.94 \[ -\frac{27}{2432} \,{\left (2 \, x + 3\right )}^{\frac{19}{2}} + \frac{567}{2176} \,{\left (2 \, x + 3\right )}^{\frac{17}{2}} - \frac{1173}{640} \,{\left (2 \, x + 3\right )}^{\frac{15}{2}} + \frac{10475}{1664} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} - \frac{17201}{1408} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{5335}{384} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} - \frac{7925}{896} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{325}{128} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^3*(2*x + 3)^(3/2)*(x - 5),x, algorithm="giac")
[Out]