Optimal. Leaf size=79 \[ -\frac{9}{544} (2 x+3)^{17/2}+\frac{11}{32} (2 x+3)^{15/2}-\frac{359}{208} (2 x+3)^{13/2}+\frac{651}{176} (2 x+3)^{11/2}-\frac{355}{96} (2 x+3)^{9/2}+\frac{325}{224} (2 x+3)^{7/2} \]
[Out]
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Rubi [A] time = 0.0717024, antiderivative size = 79, 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 \[ -\frac{9}{544} (2 x+3)^{17/2}+\frac{11}{32} (2 x+3)^{15/2}-\frac{359}{208} (2 x+3)^{13/2}+\frac{651}{176} (2 x+3)^{11/2}-\frac{355}{96} (2 x+3)^{9/2}+\frac{325}{224} (2 x+3)^{7/2} \]
Antiderivative was successfully verified.
[In] Int[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 14.2332, size = 70, normalized size = 0.89 \[ - \frac{9 \left (2 x + 3\right )^{\frac{17}{2}}}{544} + \frac{11 \left (2 x + 3\right )^{\frac{15}{2}}}{32} - \frac{359 \left (2 x + 3\right )^{\frac{13}{2}}}{208} + \frac{651 \left (2 x + 3\right )^{\frac{11}{2}}}{176} - \frac{355 \left (2 x + 3\right )^{\frac{9}{2}}}{96} + \frac{325 \left (2 x + 3\right )^{\frac{7}{2}}}{224} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)*(3+2*x)**(5/2)*(3*x**2+5*x+2)**2,x)
[Out]
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Mathematica [A] time = 0.0259023, size = 38, normalized size = 0.48 \[ -\frac{(2 x+3)^{7/2} \left (27027 x^5-78078 x^4-371679 x^3-461664 x^2-236768 x-44388\right )}{51051} \]
Antiderivative was successfully verified.
[In] Integrate[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^2,x]
[Out]
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Maple [A] time = 0.007, size = 35, normalized size = 0.4 \[ -{\frac{27027\,{x}^{5}-78078\,{x}^{4}-371679\,{x}^{3}-461664\,{x}^{2}-236768\,x-44388}{51051} \left ( 3+2\,x \right ) ^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3+2*x)^(5/2)*(3*x^2+5*x+2)^2,x)
[Out]
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Maxima [A] time = 0.707673, size = 74, normalized size = 0.94 \[ -\frac{9}{544} \,{\left (2 \, x + 3\right )}^{\frac{17}{2}} + \frac{11}{32} \,{\left (2 \, x + 3\right )}^{\frac{15}{2}} - \frac{359}{208} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} + \frac{651}{176} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} - \frac{355}{96} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} + \frac{325}{224} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^2*(2*x + 3)^(5/2)*(x - 5),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.272941, size = 66, normalized size = 0.84 \[ -\frac{1}{51051} \,{\left (216216 \, x^{8} + 348348 \, x^{7} - 4324782 \, x^{6} - 20560239 \, x^{5} - 40692820 \, x^{4} - 43843941 \, x^{3} - 26848368 \, x^{2} - 8789688 \, x - 1198476\right )} \sqrt{2 \, x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^2*(2*x + 3)^(5/2)*(x - 5),x, algorithm="fricas")
[Out]
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Sympy [A] time = 12.67, size = 70, normalized size = 0.89 \[ - \frac{9 \left (2 x + 3\right )^{\frac{17}{2}}}{544} + \frac{11 \left (2 x + 3\right )^{\frac{15}{2}}}{32} - \frac{359 \left (2 x + 3\right )^{\frac{13}{2}}}{208} + \frac{651 \left (2 x + 3\right )^{\frac{11}{2}}}{176} - \frac{355 \left (2 x + 3\right )^{\frac{9}{2}}}{96} + \frac{325 \left (2 x + 3\right )^{\frac{7}{2}}}{224} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)*(3+2*x)**(5/2)*(3*x**2+5*x+2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.279012, size = 74, normalized size = 0.94 \[ -\frac{9}{544} \,{\left (2 \, x + 3\right )}^{\frac{17}{2}} + \frac{11}{32} \,{\left (2 \, x + 3\right )}^{\frac{15}{2}} - \frac{359}{208} \,{\left (2 \, x + 3\right )}^{\frac{13}{2}} + \frac{651}{176} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} - \frac{355}{96} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} + \frac{325}{224} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x^2 + 5*x + 2)^2*(2*x + 3)^(5/2)*(x - 5),x, algorithm="giac")
[Out]