3.1413 \(\int \frac{(1-2 x)^3}{(2+3 x)^5 (3+5 x)^3} \, dx\)

Optimal. Leaf size=75 \[ \frac{128634}{3 x+2}+\frac{103455}{5 x+3}+\frac{7854}{(3 x+2)^2}-\frac{6655}{2 (5 x+3)^2}+\frac{539}{(3 x+2)^3}+\frac{343}{12 (3 x+2)^4}-953535 \log (3 x+2)+953535 \log (5 x+3) \]

[Out]

343/(12*(2 + 3*x)^4) + 539/(2 + 3*x)^3 + 7854/(2 + 3*x)^2 + 128634/(2 + 3*x) - 6
655/(2*(3 + 5*x)^2) + 103455/(3 + 5*x) - 953535*Log[2 + 3*x] + 953535*Log[3 + 5*
x]

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Rubi [A]  time = 0.0936315, antiderivative size = 75, 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 \[ \frac{128634}{3 x+2}+\frac{103455}{5 x+3}+\frac{7854}{(3 x+2)^2}-\frac{6655}{2 (5 x+3)^2}+\frac{539}{(3 x+2)^3}+\frac{343}{12 (3 x+2)^4}-953535 \log (3 x+2)+953535 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3/((2 + 3*x)^5*(3 + 5*x)^3),x]

[Out]

343/(12*(2 + 3*x)^4) + 539/(2 + 3*x)^3 + 7854/(2 + 3*x)^2 + 128634/(2 + 3*x) - 6
655/(2*(3 + 5*x)^2) + 103455/(3 + 5*x) - 953535*Log[2 + 3*x] + 953535*Log[3 + 5*
x]

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Rubi in Sympy [A]  time = 12.4196, size = 66, normalized size = 0.88 \[ - 953535 \log{\left (3 x + 2 \right )} + 953535 \log{\left (5 x + 3 \right )} + \frac{103455}{5 x + 3} - \frac{6655}{2 \left (5 x + 3\right )^{2}} + \frac{128634}{3 x + 2} + \frac{7854}{\left (3 x + 2\right )^{2}} + \frac{539}{\left (3 x + 2\right )^{3}} + \frac{343}{12 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3/(2+3*x)**5/(3+5*x)**3,x)

[Out]

-953535*log(3*x + 2) + 953535*log(5*x + 3) + 103455/(5*x + 3) - 6655/(2*(5*x + 3
)**2) + 128634/(3*x + 2) + 7854/(3*x + 2)**2 + 539/(3*x + 2)**3 + 343/(12*(3*x +
2)**4)

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Mathematica [A]  time = 0.0593479, size = 77, normalized size = 1.03 \[ \frac{128634}{3 x+2}+\frac{103455}{5 x+3}+\frac{7854}{(3 x+2)^2}-\frac{6655}{2 (5 x+3)^2}+\frac{539}{(3 x+2)^3}+\frac{343}{12 (3 x+2)^4}-953535 \log (5 (3 x+2))+953535 \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^3/((2 + 3*x)^5*(3 + 5*x)^3),x]

[Out]

343/(12*(2 + 3*x)^4) + 539/(2 + 3*x)^3 + 7854/(2 + 3*x)^2 + 128634/(2 + 3*x) - 6
655/(2*(3 + 5*x)^2) + 103455/(3 + 5*x) - 953535*Log[5*(2 + 3*x)] + 953535*Log[3
+ 5*x]

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Maple [A]  time = 0.014, size = 72, normalized size = 1. \[{\frac{343}{12\, \left ( 2+3\,x \right ) ^{4}}}+539\, \left ( 2+3\,x \right ) ^{-3}+7854\, \left ( 2+3\,x \right ) ^{-2}+128634\, \left ( 2+3\,x \right ) ^{-1}-{\frac{6655}{2\, \left ( 3+5\,x \right ) ^{2}}}+103455\, \left ( 3+5\,x \right ) ^{-1}-953535\,\ln \left ( 2+3\,x \right ) +953535\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3/(2+3*x)^5/(3+5*x)^3,x)

[Out]

343/12/(2+3*x)^4+539/(2+3*x)^3+7854/(2+3*x)^2+128634/(2+3*x)-6655/2/(3+5*x)^2+10
3455/(3+5*x)-953535*ln(2+3*x)+953535*ln(3+5*x)

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Maxima [A]  time = 1.34471, size = 103, normalized size = 1.37 \[ \frac{1544726700 \, x^{5} + 4994616330 \, x^{4} + 6455813364 \, x^{3} + 4169655991 \, x^{2} + 1345680462 \, x + 173603415}{12 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} + 953535 \, \log \left (5 \, x + 3\right ) - 953535 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)^3/((5*x + 3)^3*(3*x + 2)^5),x, algorithm="maxima")

[Out]

1/12*(1544726700*x^5 + 4994616330*x^4 + 6455813364*x^3 + 4169655991*x^2 + 134568
0462*x + 173603415)/(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 13
44*x + 144) + 953535*log(5*x + 3) - 953535*log(3*x + 2)

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Fricas [A]  time = 0.204576, size = 182, normalized size = 2.43 \[ \frac{1544726700 \, x^{5} + 4994616330 \, x^{4} + 6455813364 \, x^{3} + 4169655991 \, x^{2} + 11442420 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (5 \, x + 3\right ) - 11442420 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )} \log \left (3 \, x + 2\right ) + 1345680462 \, x + 173603415}{12 \,{\left (2025 \, x^{6} + 7830 \, x^{5} + 12609 \, x^{4} + 10824 \, x^{3} + 5224 \, x^{2} + 1344 \, x + 144\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)^3/((5*x + 3)^3*(3*x + 2)^5),x, algorithm="fricas")

[Out]

1/12*(1544726700*x^5 + 4994616330*x^4 + 6455813364*x^3 + 4169655991*x^2 + 114424
20*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)*log(5
*x + 3) - 11442420*(2025*x^6 + 7830*x^5 + 12609*x^4 + 10824*x^3 + 5224*x^2 + 134
4*x + 144)*log(3*x + 2) + 1345680462*x + 173603415)/(2025*x^6 + 7830*x^5 + 12609
*x^4 + 10824*x^3 + 5224*x^2 + 1344*x + 144)

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Sympy [A]  time = 0.571914, size = 71, normalized size = 0.95 \[ \frac{1544726700 x^{5} + 4994616330 x^{4} + 6455813364 x^{3} + 4169655991 x^{2} + 1345680462 x + 173603415}{24300 x^{6} + 93960 x^{5} + 151308 x^{4} + 129888 x^{3} + 62688 x^{2} + 16128 x + 1728} + 953535 \log{\left (x + \frac{3}{5} \right )} - 953535 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3/(2+3*x)**5/(3+5*x)**3,x)

[Out]

(1544726700*x**5 + 4994616330*x**4 + 6455813364*x**3 + 4169655991*x**2 + 1345680
462*x + 173603415)/(24300*x**6 + 93960*x**5 + 151308*x**4 + 129888*x**3 + 62688*
x**2 + 16128*x + 1728) + 953535*log(x + 3/5) - 953535*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.215578, size = 103, normalized size = 1.37 \[ \frac{128634}{3 \, x + 2} - \frac{27225 \,{\left (\frac{136}{3 \, x + 2} - 625\right )}}{2 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + \frac{7854}{{\left (3 \, x + 2\right )}^{2}} + \frac{539}{{\left (3 \, x + 2\right )}^{3}} + \frac{343}{12 \,{\left (3 \, x + 2\right )}^{4}} + 953535 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(2*x - 1)^3/((5*x + 3)^3*(3*x + 2)^5),x, algorithm="giac")

[Out]

128634/(3*x + 2) - 27225/2*(136/(3*x + 2) - 625)/(1/(3*x + 2) - 5)^2 + 7854/(3*x
+ 2)^2 + 539/(3*x + 2)^3 + 343/12/(3*x + 2)^4 + 953535*ln(abs(-1/(3*x + 2) + 5)
)