3.1430 \(\int \frac{3+5 x}{(1-2 x) (2+3 x)^5} \, dx\)

Optimal. Leaf size=65 \[ -\frac{44}{2401 (3 x+2)}-\frac{11}{343 (3 x+2)^2}-\frac{11}{147 (3 x+2)^3}+\frac{1}{84 (3 x+2)^4}-\frac{88 \log (1-2 x)}{16807}+\frac{88 \log (3 x+2)}{16807} \]

[Out]

1/(84*(2 + 3*x)^4) - 11/(147*(2 + 3*x)^3) - 11/(343*(2 + 3*x)^2) - 44/(2401*(2 +
3*x)) - (88*Log[1 - 2*x])/16807 + (88*Log[2 + 3*x])/16807

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Rubi [A]  time = 0.0621381, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{44}{2401 (3 x+2)}-\frac{11}{343 (3 x+2)^2}-\frac{11}{147 (3 x+2)^3}+\frac{1}{84 (3 x+2)^4}-\frac{88 \log (1-2 x)}{16807}+\frac{88 \log (3 x+2)}{16807} \]

Antiderivative was successfully verified.

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

[Out]

1/(84*(2 + 3*x)^4) - 11/(147*(2 + 3*x)^3) - 11/(343*(2 + 3*x)^2) - 44/(2401*(2 +
3*x)) - (88*Log[1 - 2*x])/16807 + (88*Log[2 + 3*x])/16807

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Rubi in Sympy [A]  time = 9.58565, size = 56, normalized size = 0.86 \[ - \frac{88 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{88 \log{\left (3 x + 2 \right )}}{16807} - \frac{44}{2401 \left (3 x + 2\right )} - \frac{11}{343 \left (3 x + 2\right )^{2}} - \frac{11}{147 \left (3 x + 2\right )^{3}} + \frac{1}{84 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-88*log(-2*x + 1)/16807 + 88*log(3*x + 2)/16807 - 44/(2401*(3*x + 2)) - 11/(343*
(3*x + 2)**2) - 11/(147*(3*x + 2)**3) + 1/(84*(3*x + 2)**4)

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Mathematica [A]  time = 0.0493011, size = 45, normalized size = 0.69 \[ \frac{-\frac{7 \left (4752 x^3+12276 x^2+12188 x+3963\right )}{(3 x+2)^4}-352 \log (3-6 x)+352 \log (3 x+2)}{67228} \]

Antiderivative was successfully verified.

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

[Out]

((-7*(3963 + 12188*x + 12276*x^2 + 4752*x^3))/(2 + 3*x)^4 - 352*Log[3 - 6*x] + 3
52*Log[2 + 3*x])/67228

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Maple [A]  time = 0.013, size = 54, normalized size = 0.8 \[{\frac{1}{84\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{11}{147\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{11}{343\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{44}{4802+7203\,x}}+{\frac{88\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{88\,\ln \left ( -1+2\,x \right ) }{16807}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/84/(2+3*x)^4-11/147/(2+3*x)^3-11/343/(2+3*x)^2-44/2401/(2+3*x)+88/16807*ln(2+3
*x)-88/16807*ln(-1+2*x)

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Maxima [A]  time = 1.3443, size = 76, normalized size = 1.17 \[ -\frac{4752 \, x^{3} + 12276 \, x^{2} + 12188 \, x + 3963}{9604 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{88}{16807} \, \log \left (3 \, x + 2\right ) - \frac{88}{16807} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/9604*(4752*x^3 + 12276*x^2 + 12188*x + 3963)/(81*x^4 + 216*x^3 + 216*x^2 + 96
*x + 16) + 88/16807*log(3*x + 2) - 88/16807*log(2*x - 1)

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Fricas [A]  time = 0.231948, size = 128, normalized size = 1.97 \[ -\frac{33264 \, x^{3} + 85932 \, x^{2} - 352 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 352 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (2 \, x - 1\right ) + 85316 \, x + 27741}{67228 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/67228*(33264*x^3 + 85932*x^2 - 352*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*l
og(3*x + 2) + 352*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(2*x - 1) + 85316*
x + 27741)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)

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Sympy [A]  time = 0.442806, size = 54, normalized size = 0.83 \[ - \frac{4752 x^{3} + 12276 x^{2} + 12188 x + 3963}{777924 x^{4} + 2074464 x^{3} + 2074464 x^{2} + 921984 x + 153664} - \frac{88 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{88 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(4752*x**3 + 12276*x**2 + 12188*x + 3963)/(777924*x**4 + 2074464*x**3 + 2074464
*x**2 + 921984*x + 153664) - 88*log(x - 1/2)/16807 + 88*log(x + 2/3)/16807

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GIAC/XCAS [A]  time = 0.204543, size = 70, normalized size = 1.08 \[ -\frac{44}{2401 \,{\left (3 \, x + 2\right )}} - \frac{11}{343 \,{\left (3 \, x + 2\right )}^{2}} - \frac{11}{147 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1}{84 \,{\left (3 \, x + 2\right )}^{4}} - \frac{88}{16807} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-44/2401/(3*x + 2) - 11/343/(3*x + 2)^2 - 11/147/(3*x + 2)^3 + 1/84/(3*x + 2)^4
- 88/16807*ln(abs(-7/(3*x + 2) + 2))