Optimal. Leaf size=66 \[ -\frac{648 x^5}{625}+\frac{513 x^4}{625}+\frac{2826 x^3}{3125}-\frac{7617 x^2}{6250}+\frac{4691 x}{15625}-\frac{15246}{390625 (5 x+3)}-\frac{1331}{781250 (5 x+3)^2}+\frac{63294 \log (5 x+3)}{390625} \]
[Out]
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Rubi [A] time = 0.0804466, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{648 x^5}{625}+\frac{513 x^4}{625}+\frac{2826 x^3}{3125}-\frac{7617 x^2}{6250}+\frac{4691 x}{15625}-\frac{15246}{390625 (5 x+3)}-\frac{1331}{781250 (5 x+3)^2}+\frac{63294 \log (5 x+3)}{390625} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(2 + 3*x)^4)/(3 + 5*x)^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{648 x^{5}}{625} + \frac{513 x^{4}}{625} + \frac{2826 x^{3}}{3125} + \frac{63294 \log{\left (5 x + 3 \right )}}{390625} + \int \frac{4691}{15625}\, dx - \frac{7617 \int x\, dx}{3125} - \frac{15246}{390625 \left (5 x + 3\right )} - \frac{1331}{781250 \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**4/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.054782, size = 63, normalized size = 0.95 \[ \frac{-101250000 x^7-41343750 x^6+148050000 x^5+15815625 x^4-81707500 x^3+53587800 x^2+83293560 x+632940 (5 x+3)^2 \log (6 (5 x+3))+21586298}{3906250 (5 x+3)^2} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(2 + 3*x)^4)/(3 + 5*x)^3,x]
[Out]
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Maple [A] time = 0.008, size = 51, normalized size = 0.8 \[{\frac{4691\,x}{15625}}-{\frac{7617\,{x}^{2}}{6250}}+{\frac{2826\,{x}^{3}}{3125}}+{\frac{513\,{x}^{4}}{625}}-{\frac{648\,{x}^{5}}{625}}-{\frac{1331}{781250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{15246}{1171875+1953125\,x}}+{\frac{63294\,\ln \left ( 3+5\,x \right ) }{390625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^4/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.36457, size = 69, normalized size = 1.05 \[ -\frac{648}{625} \, x^{5} + \frac{513}{625} \, x^{4} + \frac{2826}{3125} \, x^{3} - \frac{7617}{6250} \, x^{2} + \frac{4691}{15625} \, x - \frac{121 \,{\left (1260 \, x + 767\right )}}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{63294}{390625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^4*(2*x - 1)^3/(5*x + 3)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207412, size = 90, normalized size = 1.36 \[ -\frac{20250000 \, x^{7} + 8268750 \, x^{6} - 29610000 \, x^{5} - 3163125 \, x^{4} + 16341500 \, x^{3} + 1532625 \, x^{2} - 126588 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 1958490 \, x + 92807}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^4*(2*x - 1)^3/(5*x + 3)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.302394, size = 56, normalized size = 0.85 \[ - \frac{648 x^{5}}{625} + \frac{513 x^{4}}{625} + \frac{2826 x^{3}}{3125} - \frac{7617 x^{2}}{6250} + \frac{4691 x}{15625} - \frac{152460 x + 92807}{19531250 x^{2} + 23437500 x + 7031250} + \frac{63294 \log{\left (5 x + 3 \right )}}{390625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**4/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.209062, size = 63, normalized size = 0.95 \[ -\frac{648}{625} \, x^{5} + \frac{513}{625} \, x^{4} + \frac{2826}{3125} \, x^{3} - \frac{7617}{6250} \, x^{2} + \frac{4691}{15625} \, x - \frac{121 \,{\left (1260 \, x + 767\right )}}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{63294}{390625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^4*(2*x - 1)^3/(5*x + 3)^3,x, algorithm="giac")
[Out]