Optimal. Leaf size=47 \[ \frac{1124 (6 x+5)}{9 \sqrt{3 x^2+5 x+2}}-\frac{2 (139 x+121)}{9 \left (3 x^2+5 x+2\right )^{3/2}} \]
[Out]
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Rubi [A] time = 0.0592359, antiderivative size = 47, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08 \[ \frac{1124 (6 x+5)}{9 \sqrt{3 x^2+5 x+2}}-\frac{2 (139 x+121)}{9 \left (3 x^2+5 x+2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 8.33083, size = 39, normalized size = 0.83 \[ \frac{562 \left (12 x + 10\right )}{9 \sqrt{3 x^{2} + 5 x + 2}} - \frac{2 \left (139 x + 121\right )}{9 \left (3 x^{2} + 5 x + 2\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)*(3+2*x)/(3*x**2+5*x+2)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0314921, size = 31, normalized size = 0.66 \[ \frac{2 \left (1124 x^3+2810 x^2+2295 x+611\right )}{\left (3 x^2+5 x+2\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^(5/2),x]
[Out]
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Maple [A] time = 0.006, size = 38, normalized size = 0.8 \[ 2\,{\frac{ \left ( 1124\,{x}^{3}+2810\,{x}^{2}+2295\,x+611 \right ) \left ( 1+x \right ) \left ( 2+3\,x \right ) }{ \left ( 3\,{x}^{2}+5\,x+2 \right ) ^{5/2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3+2*x)/(3*x^2+5*x+2)^(5/2),x)
[Out]
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Maxima [A] time = 0.710899, size = 80, normalized size = 1.7 \[ \frac{2248 \, x}{3 \, \sqrt{3 \, x^{2} + 5 \, x + 2}} + \frac{5620}{9 \, \sqrt{3 \, x^{2} + 5 \, x + 2}} - \frac{278 \, x}{9 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{3}{2}}} - \frac{242}{9 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)*(x - 5)/(3*x^2 + 5*x + 2)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.276964, size = 69, normalized size = 1.47 \[ \frac{2 \,{\left (1124 \, x^{3} + 2810 \, x^{2} + 2295 \, x + 611\right )} \sqrt{3 \, x^{2} + 5 \, x + 2}}{9 \, x^{4} + 30 \, x^{3} + 37 \, x^{2} + 20 \, x + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)*(x - 5)/(3*x^2 + 5*x + 2)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \int \left (- \frac{7 x}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right )\, dx - \int \frac{2 x^{2}}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\, dx - \int \left (- \frac{15}{9 x^{4} \sqrt{3 x^{2} + 5 x + 2} + 30 x^{3} \sqrt{3 x^{2} + 5 x + 2} + 37 x^{2} \sqrt{3 x^{2} + 5 x + 2} + 20 x \sqrt{3 x^{2} + 5 x + 2} + 4 \sqrt{3 x^{2} + 5 x + 2}}\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)*(3+2*x)/(3*x**2+5*x+2)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.277025, size = 38, normalized size = 0.81 \[ \frac{2 \,{\left ({\left (562 \,{\left (2 \, x + 5\right )} x + 2295\right )} x + 611\right )}}{{\left (3 \, x^{2} + 5 \, x + 2\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)*(x - 5)/(3*x^2 + 5*x + 2)^(5/2),x, algorithm="giac")
[Out]