Optimal. Leaf size=70 \[ \frac{8 x^5}{25}-\frac{21 x^4}{25}+\frac{1222 x^3}{375}-\frac{7451 x^2}{1250}-\frac{158389 \log \left (5 x^2+3 x+2\right )}{31250}+\frac{49508 x}{3125}+\frac{328757 \tan ^{-1}\left (\frac{10 x+3}{\sqrt{31}}\right )}{15625 \sqrt{31}} \]
[Out]
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Rubi [A] time = 0.102539, antiderivative size = 70, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{8 x^5}{25}-\frac{21 x^4}{25}+\frac{1222 x^3}{375}-\frac{7451 x^2}{1250}-\frac{158389 \log \left (5 x^2+3 x+2\right )}{31250}+\frac{49508 x}{3125}+\frac{328757 \tan ^{-1}\left (\frac{10 x+3}{\sqrt{31}}\right )}{15625 \sqrt{31}} \]
Antiderivative was successfully verified.
[In] Int[(3 - x + 2*x^2)^3/(2 + 3*x + 5*x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{637 x^{3}}{375} - \frac{\left (- 40 x + 65\right ) \left (2 x^{2} - x + 3\right )^{2}}{500} - \frac{158389 \log{\left (5 x^{2} + 3 x + 2 \right )}}{31250} + \frac{328757 \sqrt{31} \operatorname{atan}{\left (\sqrt{31} \left (\frac{10 x}{31} + \frac{3}{31}\right ) \right )}}{484375} - \frac{\int \left (- \frac{179282}{25}\right )\, dx}{500} - \frac{9477 \int x\, dx}{1250} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*x**2-x+3)**3/(5*x**2+3*x+2),x)
[Out]
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Mathematica [A] time = 0.040395, size = 63, normalized size = 0.9 \[ \frac{31 \left (5 x \left (6000 x^4-15750 x^3+61100 x^2-111765 x+297048\right )-475167 \log \left (5 x^2+3 x+2\right )\right )+1972542 \sqrt{31} \tan ^{-1}\left (\frac{10 x+3}{\sqrt{31}}\right )}{2906250} \]
Antiderivative was successfully verified.
[In] Integrate[(3 - x + 2*x^2)^3/(2 + 3*x + 5*x^2),x]
[Out]
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Maple [A] time = 0.005, size = 54, normalized size = 0.8 \[{\frac{49508\,x}{3125}}-{\frac{7451\,{x}^{2}}{1250}}+{\frac{1222\,{x}^{3}}{375}}-{\frac{21\,{x}^{4}}{25}}+{\frac{8\,{x}^{5}}{25}}-{\frac{158389\,\ln \left ( 5\,{x}^{2}+3\,x+2 \right ) }{31250}}+{\frac{328757\,\sqrt{31}}{484375}\arctan \left ({\frac{ \left ( 3+10\,x \right ) \sqrt{31}}{31}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*x^2-x+3)^3/(5*x^2+3*x+2),x)
[Out]
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Maxima [A] time = 0.768738, size = 72, normalized size = 1.03 \[ \frac{8}{25} \, x^{5} - \frac{21}{25} \, x^{4} + \frac{1222}{375} \, x^{3} - \frac{7451}{1250} \, x^{2} + \frac{328757}{484375} \, \sqrt{31} \arctan \left (\frac{1}{31} \, \sqrt{31}{\left (10 \, x + 3\right )}\right ) + \frac{49508}{3125} \, x - \frac{158389}{31250} \, \log \left (5 \, x^{2} + 3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 - x + 3)^3/(5*x^2 + 3*x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.262724, size = 86, normalized size = 1.23 \[ \frac{1}{2906250} \, \sqrt{31}{\left (5 \, \sqrt{31}{\left (6000 \, x^{5} - 15750 \, x^{4} + 61100 \, x^{3} - 111765 \, x^{2} + 297048 \, x\right )} - 475167 \, \sqrt{31} \log \left (5 \, x^{2} + 3 \, x + 2\right ) + 1972542 \, \arctan \left (\frac{1}{31} \, \sqrt{31}{\left (10 \, x + 3\right )}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 - x + 3)^3/(5*x^2 + 3*x + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.158155, size = 76, normalized size = 1.09 \[ \frac{8 x^{5}}{25} - \frac{21 x^{4}}{25} + \frac{1222 x^{3}}{375} - \frac{7451 x^{2}}{1250} + \frac{49508 x}{3125} - \frac{158389 \log{\left (x^{2} + \frac{3 x}{5} + \frac{2}{5} \right )}}{31250} + \frac{328757 \sqrt{31} \operatorname{atan}{\left (\frac{10 \sqrt{31} x}{31} + \frac{3 \sqrt{31}}{31} \right )}}{484375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x**2-x+3)**3/(5*x**2+3*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.265556, size = 72, normalized size = 1.03 \[ \frac{8}{25} \, x^{5} - \frac{21}{25} \, x^{4} + \frac{1222}{375} \, x^{3} - \frac{7451}{1250} \, x^{2} + \frac{328757}{484375} \, \sqrt{31} \arctan \left (\frac{1}{31} \, \sqrt{31}{\left (10 \, x + 3\right )}\right ) + \frac{49508}{3125} \, x - \frac{158389}{31250} \,{\rm ln}\left (5 \, x^{2} + 3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^2 - x + 3)^3/(5*x^2 + 3*x + 2),x, algorithm="giac")
[Out]