3.1688 \(\int \frac{2+3 x}{(1-2 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=65 \[ \frac{144}{14641 (1-2 x)}-\frac{195}{14641 (5 x+3)}+\frac{7}{1331 (1-2 x)^2}-\frac{5}{2662 (5 x+3)^2}-\frac{1110 \log (1-2 x)}{161051}+\frac{1110 \log (5 x+3)}{161051} \]

[Out]

7/(1331*(1 - 2*x)^2) + 144/(14641*(1 - 2*x)) - 5/(2662*(3 + 5*x)^2) - 195/(14641
*(3 + 5*x)) - (1110*Log[1 - 2*x])/161051 + (1110*Log[3 + 5*x])/161051

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Rubi [A]  time = 0.068596, 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 \[ \frac{144}{14641 (1-2 x)}-\frac{195}{14641 (5 x+3)}+\frac{7}{1331 (1-2 x)^2}-\frac{5}{2662 (5 x+3)^2}-\frac{1110 \log (1-2 x)}{161051}+\frac{1110 \log (5 x+3)}{161051} \]

Antiderivative was successfully verified.

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

[Out]

7/(1331*(1 - 2*x)^2) + 144/(14641*(1 - 2*x)) - 5/(2662*(3 + 5*x)^2) - 195/(14641
*(3 + 5*x)) - (1110*Log[1 - 2*x])/161051 + (1110*Log[3 + 5*x])/161051

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Rubi in Sympy [A]  time = 9.87283, size = 53, normalized size = 0.82 \[ - \frac{1110 \log{\left (- 2 x + 1 \right )}}{161051} + \frac{1110 \log{\left (5 x + 3 \right )}}{161051} - \frac{195}{14641 \left (5 x + 3\right )} - \frac{5}{2662 \left (5 x + 3\right )^{2}} + \frac{144}{14641 \left (- 2 x + 1\right )} + \frac{7}{1331 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1110*log(-2*x + 1)/161051 + 1110*log(5*x + 3)/161051 - 195/(14641*(5*x + 3)) -
5/(2662*(5*x + 3)**2) + 144/(14641*(-2*x + 1)) + 7/(1331*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0397905, size = 48, normalized size = 0.74 \[ \frac{\frac{11 \left (-22200 x^3-3330 x^2+11026 x+2753\right )}{\left (10 x^2+x-3\right )^2}-2220 \log (1-2 x)+2220 \log (5 x+3)}{322102} \]

Antiderivative was successfully verified.

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

[Out]

((11*(2753 + 11026*x - 3330*x^2 - 22200*x^3))/(-3 + x + 10*x^2)^2 - 2220*Log[1 -
2*x] + 2220*Log[3 + 5*x])/322102

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Maple [A]  time = 0.014, size = 54, normalized size = 0.8 \[ -{\frac{5}{2662\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{195}{43923+73205\,x}}+{\frac{1110\,\ln \left ( 3+5\,x \right ) }{161051}}+{\frac{7}{1331\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{144}{-14641+29282\,x}}-{\frac{1110\,\ln \left ( -1+2\,x \right ) }{161051}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-5/2662/(3+5*x)^2-195/14641/(3+5*x)+1110/161051*ln(3+5*x)+7/1331/(-1+2*x)^2-144/
14641/(-1+2*x)-1110/161051*ln(-1+2*x)

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Maxima [A]  time = 1.35055, size = 76, normalized size = 1.17 \[ -\frac{22200 \, x^{3} + 3330 \, x^{2} - 11026 \, x - 2753}{29282 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{1110}{161051} \, \log \left (5 \, x + 3\right ) - \frac{1110}{161051} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/29282*(22200*x^3 + 3330*x^2 - 11026*x - 2753)/(100*x^4 + 20*x^3 - 59*x^2 - 6*
x + 9) + 1110/161051*log(5*x + 3) - 1110/161051*log(2*x - 1)

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Fricas [A]  time = 0.20892, size = 128, normalized size = 1.97 \[ -\frac{244200 \, x^{3} + 36630 \, x^{2} - 2220 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2220 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 121286 \, x - 30283}{322102 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/322102*(244200*x^3 + 36630*x^2 - 2220*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*l
og(5*x + 3) + 2220*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) - 121286*x
- 30283)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)

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Sympy [A]  time = 0.421865, size = 54, normalized size = 0.83 \[ - \frac{22200 x^{3} + 3330 x^{2} - 11026 x - 2753}{2928200 x^{4} + 585640 x^{3} - 1727638 x^{2} - 175692 x + 263538} - \frac{1110 \log{\left (x - \frac{1}{2} \right )}}{161051} + \frac{1110 \log{\left (x + \frac{3}{5} \right )}}{161051} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(22200*x**3 + 3330*x**2 - 11026*x - 2753)/(2928200*x**4 + 585640*x**3 - 1727638
*x**2 - 175692*x + 263538) - 1110*log(x - 1/2)/161051 + 1110*log(x + 3/5)/161051

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GIAC/XCAS [A]  time = 0.212943, size = 62, normalized size = 0.95 \[ -\frac{22200 \, x^{3} + 3330 \, x^{2} - 11026 \, x - 2753}{29282 \,{\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac{1110}{161051} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{1110}{161051} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/29282*(22200*x^3 + 3330*x^2 - 11026*x - 2753)/(10*x^2 + x - 3)^2 + 1110/16105
1*ln(abs(5*x + 3)) - 1110/161051*ln(abs(2*x - 1))