Optimal. Leaf size=34 \[ \frac{10}{81 (3 x+2)^3}-\frac{37}{108 (3 x+2)^4}+\frac{7}{135 (3 x+2)^5} \]
[Out]
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Rubi [A] time = 0.037511, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ \frac{10}{81 (3 x+2)^3}-\frac{37}{108 (3 x+2)^4}+\frac{7}{135 (3 x+2)^5} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^6,x]
[Out]
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Rubi in Sympy [A] time = 6.49375, size = 29, normalized size = 0.85 \[ \frac{10}{81 \left (3 x + 2\right )^{3}} - \frac{37}{108 \left (3 x + 2\right )^{4}} + \frac{7}{135 \left (3 x + 2\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(3+5*x)/(2+3*x)**6,x)
[Out]
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Mathematica [A] time = 0.00985068, size = 21, normalized size = 0.62 \[ \frac{1800 x^2+735 x-226}{1620 (3 x+2)^5} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(3 + 5*x))/(2 + 3*x)^6,x]
[Out]
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Maple [A] time = 0.007, size = 29, normalized size = 0.9 \[{\frac{7}{135\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{37}{108\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{10}{81\, \left ( 2+3\,x \right ) ^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(3+5*x)/(2+3*x)^6,x)
[Out]
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Maxima [A] time = 1.33311, size = 53, normalized size = 1.56 \[ \frac{1800 \, x^{2} + 735 \, x - 226}{1620 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(2*x - 1)/(3*x + 2)^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.206423, size = 53, normalized size = 1.56 \[ \frac{1800 \, x^{2} + 735 \, x - 226}{1620 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(2*x - 1)/(3*x + 2)^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.342035, size = 34, normalized size = 1. \[ \frac{1800 x^{2} + 735 x - 226}{393660 x^{5} + 1312200 x^{4} + 1749600 x^{3} + 1166400 x^{2} + 388800 x + 51840} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(3+5*x)/(2+3*x)**6,x)
[Out]
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GIAC/XCAS [A] time = 0.212411, size = 26, normalized size = 0.76 \[ \frac{1800 \, x^{2} + 735 \, x - 226}{1620 \,{\left (3 \, x + 2\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)*(2*x - 1)/(3*x + 2)^6,x, algorithm="giac")
[Out]