Optimal. Leaf size=56 \[ -\frac{100}{729 (3 x+2)^3}+\frac{185}{243 (3 x+2)^4}-\frac{503}{405 (3 x+2)^5}+\frac{259}{729 (3 x+2)^6}-\frac{7}{243 (3 x+2)^7} \]
[Out]
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Rubi [A] time = 0.061958, antiderivative size = 56, 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 \[ -\frac{100}{729 (3 x+2)^3}+\frac{185}{243 (3 x+2)^4}-\frac{503}{405 (3 x+2)^5}+\frac{259}{729 (3 x+2)^6}-\frac{7}{243 (3 x+2)^7} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^8,x]
[Out]
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Rubi in Sympy [A] time = 10.1682, size = 49, normalized size = 0.88 \[ - \frac{100}{729 \left (3 x + 2\right )^{3}} + \frac{185}{243 \left (3 x + 2\right )^{4}} - \frac{503}{405 \left (3 x + 2\right )^{5}} + \frac{259}{729 \left (3 x + 2\right )^{6}} - \frac{7}{243 \left (3 x + 2\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(3+5*x)**2/(2+3*x)**8,x)
[Out]
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Mathematica [A] time = 0.0206623, size = 31, normalized size = 0.55 \[ \frac{-40500 x^4-33075 x^3+1107 x^2+1461 x-1423}{3645 (3 x+2)^7} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(3 + 5*x)^2)/(2 + 3*x)^8,x]
[Out]
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Maple [A] time = 0.007, size = 47, normalized size = 0.8 \[ -{\frac{7}{243\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{259}{729\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{503}{405\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{185}{243\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{100}{729\, \left ( 2+3\,x \right ) ^{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(3+5*x)^2/(2+3*x)^8,x)
[Out]
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Maxima [A] time = 1.3508, size = 80, normalized size = 1.43 \[ -\frac{40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.198245, size = 80, normalized size = 1.43 \[ -\frac{40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.486955, size = 56, normalized size = 1. \[ - \frac{40500 x^{4} + 33075 x^{3} - 1107 x^{2} - 1461 x + 1423}{7971615 x^{7} + 37200870 x^{6} + 74401740 x^{5} + 82668600 x^{4} + 55112400 x^{3} + 22044960 x^{2} + 4898880 x + 466560} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(3+5*x)**2/(2+3*x)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.206224, size = 39, normalized size = 0.7 \[ -\frac{40500 \, x^{4} + 33075 \, x^{3} - 1107 \, x^{2} - 1461 \, x + 1423}{3645 \,{\left (3 \, x + 2\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2*(2*x - 1)^2/(3*x + 2)^8,x, algorithm="giac")
[Out]