3.1652 \(\int \frac{(3+5 x)^3}{(1-2 x)^3 (2+3 x)^4} \, dx\)

Optimal. Leaf size=76 \[ \frac{3267}{16807 (1-2 x)}+\frac{1023}{16807 (3 x+2)}+\frac{1331}{4802 (1-2 x)^2}-\frac{33}{4802 (3 x+2)^2}+\frac{1}{3087 (3 x+2)^3}-\frac{7755 \log (1-2 x)}{117649}+\frac{7755 \log (3 x+2)}{117649} \]

[Out]

1331/(4802*(1 - 2*x)^2) + 3267/(16807*(1 - 2*x)) + 1/(3087*(2 + 3*x)^3) - 33/(48
02*(2 + 3*x)^2) + 1023/(16807*(2 + 3*x)) - (7755*Log[1 - 2*x])/117649 + (7755*Lo
g[2 + 3*x])/117649

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Rubi [A]  time = 0.0869663, antiderivative size = 76, 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 \[ \frac{3267}{16807 (1-2 x)}+\frac{1023}{16807 (3 x+2)}+\frac{1331}{4802 (1-2 x)^2}-\frac{33}{4802 (3 x+2)^2}+\frac{1}{3087 (3 x+2)^3}-\frac{7755 \log (1-2 x)}{117649}+\frac{7755 \log (3 x+2)}{117649} \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^4),x]

[Out]

1331/(4802*(1 - 2*x)^2) + 3267/(16807*(1 - 2*x)) + 1/(3087*(2 + 3*x)^3) - 33/(48
02*(2 + 3*x)^2) + 1023/(16807*(2 + 3*x)) - (7755*Log[1 - 2*x])/117649 + (7755*Lo
g[2 + 3*x])/117649

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Rubi in Sympy [A]  time = 11.6014, size = 63, normalized size = 0.83 \[ - \frac{7755 \log{\left (- 2 x + 1 \right )}}{117649} + \frac{7755 \log{\left (3 x + 2 \right )}}{117649} + \frac{1023}{16807 \left (3 x + 2\right )} - \frac{33}{4802 \left (3 x + 2\right )^{2}} + \frac{1}{3087 \left (3 x + 2\right )^{3}} + \frac{3267}{16807 \left (- 2 x + 1\right )} + \frac{1331}{4802 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3+5*x)**3/(1-2*x)**3/(2+3*x)**4,x)

[Out]

-7755*log(-2*x + 1)/117649 + 7755*log(3*x + 2)/117649 + 1023/(16807*(3*x + 2)) -
33/(4802*(3*x + 2)**2) + 1/(3087*(3*x + 2)**3) + 3267/(16807*(-2*x + 1)) + 1331
/(4802*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0898906, size = 57, normalized size = 0.75 \[ \frac{\frac{7 \left (-2512620 x^4-2303235 x^3+3054740 x^2+4131175 x+1210868\right )}{(1-2 x)^2 (3 x+2)^3}-139590 \log (1-2 x)+139590 \log (6 x+4)}{2117682} \]

Antiderivative was successfully verified.

[In]  Integrate[(3 + 5*x)^3/((1 - 2*x)^3*(2 + 3*x)^4),x]

[Out]

((7*(1210868 + 4131175*x + 3054740*x^2 - 2303235*x^3 - 2512620*x^4))/((1 - 2*x)^
2*(2 + 3*x)^3) - 139590*Log[1 - 2*x] + 139590*Log[4 + 6*x])/2117682

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Maple [A]  time = 0.015, size = 63, normalized size = 0.8 \[{\frac{1}{3087\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{33}{4802\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{1023}{33614+50421\,x}}+{\frac{7755\,\ln \left ( 2+3\,x \right ) }{117649}}+{\frac{1331}{4802\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{3267}{-16807+33614\,x}}-{\frac{7755\,\ln \left ( -1+2\,x \right ) }{117649}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^3/(1-2*x)^3/(2+3*x)^4,x)

[Out]

1/3087/(2+3*x)^3-33/4802/(2+3*x)^2+1023/16807/(2+3*x)+7755/117649*ln(2+3*x)+1331
/4802/(-1+2*x)^2-3267/16807/(-1+2*x)-7755/117649*ln(-1+2*x)

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Maxima [A]  time = 1.34516, size = 89, normalized size = 1.17 \[ -\frac{2512620 \, x^{4} + 2303235 \, x^{3} - 3054740 \, x^{2} - 4131175 \, x - 1210868}{302526 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} + \frac{7755}{117649} \, \log \left (3 \, x + 2\right ) - \frac{7755}{117649} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3/((3*x + 2)^4*(2*x - 1)^3),x, algorithm="maxima")

[Out]

-1/302526*(2512620*x^4 + 2303235*x^3 - 3054740*x^2 - 4131175*x - 1210868)/(108*x
^5 + 108*x^4 - 45*x^3 - 58*x^2 + 4*x + 8) + 7755/117649*log(3*x + 2) - 7755/1176
49*log(2*x - 1)

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Fricas [A]  time = 0.215503, size = 155, normalized size = 2.04 \[ -\frac{17588340 \, x^{4} + 16122645 \, x^{3} - 21383180 \, x^{2} - 139590 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 139590 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (2 \, x - 1\right ) - 28918225 \, x - 8476076}{2117682 \,{\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3/((3*x + 2)^4*(2*x - 1)^3),x, algorithm="fricas")

[Out]

-1/2117682*(17588340*x^4 + 16122645*x^3 - 21383180*x^2 - 139590*(108*x^5 + 108*x
^4 - 45*x^3 - 58*x^2 + 4*x + 8)*log(3*x + 2) + 139590*(108*x^5 + 108*x^4 - 45*x^
3 - 58*x^2 + 4*x + 8)*log(2*x - 1) - 28918225*x - 8476076)/(108*x^5 + 108*x^4 -
45*x^3 - 58*x^2 + 4*x + 8)

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Sympy [A]  time = 0.524671, size = 65, normalized size = 0.86 \[ - \frac{2512620 x^{4} + 2303235 x^{3} - 3054740 x^{2} - 4131175 x - 1210868}{32672808 x^{5} + 32672808 x^{4} - 13613670 x^{3} - 17546508 x^{2} + 1210104 x + 2420208} - \frac{7755 \log{\left (x - \frac{1}{2} \right )}}{117649} + \frac{7755 \log{\left (x + \frac{2}{3} \right )}}{117649} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)**3/(1-2*x)**3/(2+3*x)**4,x)

[Out]

-(2512620*x**4 + 2303235*x**3 - 3054740*x**2 - 4131175*x - 1210868)/(32672808*x*
*5 + 32672808*x**4 - 13613670*x**3 - 17546508*x**2 + 1210104*x + 2420208) - 7755
*log(x - 1/2)/117649 + 7755*log(x + 2/3)/117649

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GIAC/XCAS [A]  time = 0.209082, size = 74, normalized size = 0.97 \[ -\frac{2512620 \, x^{4} + 2303235 \, x^{3} - 3054740 \, x^{2} - 4131175 \, x - 1210868}{302526 \,{\left (3 \, x + 2\right )}^{3}{\left (2 \, x - 1\right )}^{2}} + \frac{7755}{117649} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{7755}{117649} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3/((3*x + 2)^4*(2*x - 1)^3),x, algorithm="giac")

[Out]

-1/302526*(2512620*x^4 + 2303235*x^3 - 3054740*x^2 - 4131175*x - 1210868)/((3*x
+ 2)^3*(2*x - 1)^2) + 7755/117649*ln(abs(3*x + 2)) - 7755/117649*ln(abs(2*x - 1)
)