3.1686 \(\int \frac{(2+3 x)^3}{(1-2 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=65 \[ \frac{147}{14641 (1-2 x)}-\frac{21}{14641 (5 x+3)}+\frac{343}{5324 (1-2 x)^2}-\frac{1}{13310 (5 x+3)^2}-\frac{777 \log (1-2 x)}{161051}+\frac{777 \log (5 x+3)}{161051} \]

[Out]

343/(5324*(1 - 2*x)^2) + 147/(14641*(1 - 2*x)) - 1/(13310*(3 + 5*x)^2) - 21/(146
41*(3 + 5*x)) - (777*Log[1 - 2*x])/161051 + (777*Log[3 + 5*x])/161051

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Rubi [A]  time = 0.078504, antiderivative size = 65, 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 \[ \frac{147}{14641 (1-2 x)}-\frac{21}{14641 (5 x+3)}+\frac{343}{5324 (1-2 x)^2}-\frac{1}{13310 (5 x+3)^2}-\frac{777 \log (1-2 x)}{161051}+\frac{777 \log (5 x+3)}{161051} \]

Antiderivative was successfully verified.

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

[Out]

343/(5324*(1 - 2*x)^2) + 147/(14641*(1 - 2*x)) - 1/(13310*(3 + 5*x)^2) - 21/(146
41*(3 + 5*x)) - (777*Log[1 - 2*x])/161051 + (777*Log[3 + 5*x])/161051

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Rubi in Sympy [A]  time = 10.2658, size = 53, normalized size = 0.82 \[ - \frac{777 \log{\left (- 2 x + 1 \right )}}{161051} + \frac{777 \log{\left (5 x + 3 \right )}}{161051} - \frac{21}{14641 \left (5 x + 3\right )} - \frac{1}{13310 \left (5 x + 3\right )^{2}} + \frac{147}{14641 \left (- 2 x + 1\right )} + \frac{343}{5324 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-777*log(-2*x + 1)/161051 + 777*log(5*x + 3)/161051 - 21/(14641*(5*x + 3)) - 1/(
13310*(5*x + 3)**2) + 147/(14641*(-2*x + 1)) + 343/(5324*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0515681, size = 48, normalized size = 0.74 \[ \frac{-\frac{11 \left (155400 x^3-371997 x^2-604258 x-194963\right )}{\left (10 x^2+x-3\right )^2}+15540 \log (-5 x-3)-15540 \log (1-2 x)}{3221020} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(-194963 - 604258*x - 371997*x^2 + 155400*x^3))/(-3 + x + 10*x^2)^2 + 1554
0*Log[-3 - 5*x] - 15540*Log[1 - 2*x])/3221020

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Maple [A]  time = 0.016, size = 54, normalized size = 0.8 \[ -{\frac{1}{13310\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{21}{43923+73205\,x}}+{\frac{777\,\ln \left ( 3+5\,x \right ) }{161051}}+{\frac{343}{5324\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{147}{-14641+29282\,x}}-{\frac{777\,\ln \left ( -1+2\,x \right ) }{161051}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/13310/(3+5*x)^2-21/14641/(3+5*x)+777/161051*ln(3+5*x)+343/5324/(-1+2*x)^2-147
/14641/(-1+2*x)-777/161051*ln(-1+2*x)

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Maxima [A]  time = 1.34191, size = 76, normalized size = 1.17 \[ -\frac{155400 \, x^{3} - 371997 \, x^{2} - 604258 \, x - 194963}{292820 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{777}{161051} \, \log \left (5 \, x + 3\right ) - \frac{777}{161051} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/292820*(155400*x^3 - 371997*x^2 - 604258*x - 194963)/(100*x^4 + 20*x^3 - 59*x
^2 - 6*x + 9) + 777/161051*log(5*x + 3) - 777/161051*log(2*x - 1)

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Fricas [A]  time = 0.203042, size = 128, normalized size = 1.97 \[ -\frac{1709400 \, x^{3} - 4091967 \, x^{2} - 15540 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 15540 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 6646838 \, x - 2144593}{3221020 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3221020*(1709400*x^3 - 4091967*x^2 - 15540*(100*x^4 + 20*x^3 - 59*x^2 - 6*x +
9)*log(5*x + 3) + 15540*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) - 66
46838*x - 2144593)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)

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Sympy [A]  time = 0.483399, size = 54, normalized size = 0.83 \[ - \frac{155400 x^{3} - 371997 x^{2} - 604258 x - 194963}{29282000 x^{4} + 5856400 x^{3} - 17276380 x^{2} - 1756920 x + 2635380} - \frac{777 \log{\left (x - \frac{1}{2} \right )}}{161051} + \frac{777 \log{\left (x + \frac{3}{5} \right )}}{161051} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(155400*x**3 - 371997*x**2 - 604258*x - 194963)/(29282000*x**4 + 5856400*x**3 -
17276380*x**2 - 1756920*x + 2635380) - 777*log(x - 1/2)/161051 + 777*log(x + 3/
5)/161051

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GIAC/XCAS [A]  time = 0.209384, size = 62, normalized size = 0.95 \[ -\frac{155400 \, x^{3} - 371997 \, x^{2} - 604258 \, x - 194963}{292820 \,{\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac{777}{161051} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{777}{161051} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/292820*(155400*x^3 - 371997*x^2 - 604258*x - 194963)/(10*x^2 + x - 3)^2 + 777
/161051*ln(abs(5*x + 3)) - 777/161051*ln(abs(2*x - 1))