3.1509 \(\int \frac{1}{(1-2 x) (2+3 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=64 \[ \frac{27}{7 (3 x+2)}+\frac{1600}{121 (5 x+3)}-\frac{25}{22 (5 x+3)^2}-\frac{16 \log (1-2 x)}{65219}-\frac{2889}{49} \log (3 x+2)+\frac{78475 \log (5 x+3)}{1331} \]

[Out]

27/(7*(2 + 3*x)) - 25/(22*(3 + 5*x)^2) + 1600/(121*(3 + 5*x)) - (16*Log[1 - 2*x]
)/65219 - (2889*Log[2 + 3*x])/49 + (78475*Log[3 + 5*x])/1331

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Rubi [A]  time = 0.0744399, antiderivative size = 64, 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 \[ \frac{27}{7 (3 x+2)}+\frac{1600}{121 (5 x+3)}-\frac{25}{22 (5 x+3)^2}-\frac{16 \log (1-2 x)}{65219}-\frac{2889}{49} \log (3 x+2)+\frac{78475 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

27/(7*(2 + 3*x)) - 25/(22*(3 + 5*x)^2) + 1600/(121*(3 + 5*x)) - (16*Log[1 - 2*x]
)/65219 - (2889*Log[2 + 3*x])/49 + (78475*Log[3 + 5*x])/1331

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Rubi in Sympy [A]  time = 10.0544, size = 53, normalized size = 0.83 \[ - \frac{16 \log{\left (- 2 x + 1 \right )}}{65219} - \frac{2889 \log{\left (3 x + 2 \right )}}{49} + \frac{78475 \log{\left (5 x + 3 \right )}}{1331} + \frac{1600}{121 \left (5 x + 3\right )} - \frac{25}{22 \left (5 x + 3\right )^{2}} + \frac{27}{7 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-16*log(-2*x + 1)/65219 - 2889*log(3*x + 2)/49 + 78475*log(5*x + 3)/1331 + 1600/
(121*(5*x + 3)) - 25/(22*(5*x + 3)**2) + 27/(7*(3*x + 2))

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Mathematica [A]  time = 0.0441305, size = 60, normalized size = 0.94 \[ \frac{27}{21 x+14}+\frac{1600}{605 x+363}-\frac{25}{22 (5 x+3)^2}-\frac{16 \log (1-2 x)}{65219}-\frac{2889}{49} \log (6 x+4)+\frac{78475 \log (10 x+6)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

-25/(22*(3 + 5*x)^2) + 27/(14 + 21*x) + 1600/(363 + 605*x) - (16*Log[1 - 2*x])/6
5219 - (2889*Log[4 + 6*x])/49 + (78475*Log[6 + 10*x])/1331

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Maple [A]  time = 0.019, size = 53, normalized size = 0.8 \[ -{\frac{25}{22\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{1600}{363+605\,x}}+{\frac{78475\,\ln \left ( 3+5\,x \right ) }{1331}}+{\frac{27}{14+21\,x}}-{\frac{2889\,\ln \left ( 2+3\,x \right ) }{49}}-{\frac{16\,\ln \left ( -1+2\,x \right ) }{65219}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25/22/(3+5*x)^2+1600/121/(3+5*x)+78475/1331*ln(3+5*x)+27/7/(2+3*x)-2889/49*ln(2
+3*x)-16/65219*ln(-1+2*x)

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Maxima [A]  time = 1.34343, size = 73, normalized size = 1.14 \[ \frac{499350 \, x^{2} + 615845 \, x + 189356}{1694 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + \frac{78475}{1331} \, \log \left (5 \, x + 3\right ) - \frac{2889}{49} \, \log \left (3 \, x + 2\right ) - \frac{16}{65219} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/1694*(499350*x^2 + 615845*x + 189356)/(75*x^3 + 140*x^2 + 87*x + 18) + 78475/1
331*log(5*x + 3) - 2889/49*log(3*x + 2) - 16/65219*log(2*x - 1)

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Fricas [A]  time = 0.214556, size = 132, normalized size = 2.06 \[ \frac{38449950 \, x^{2} + 7690550 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 7690518 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) - 32 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (2 \, x - 1\right ) + 47420065 \, x + 14580412}{130438 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/130438*(38449950*x^2 + 7690550*(75*x^3 + 140*x^2 + 87*x + 18)*log(5*x + 3) - 7
690518*(75*x^3 + 140*x^2 + 87*x + 18)*log(3*x + 2) - 32*(75*x^3 + 140*x^2 + 87*x
+ 18)*log(2*x - 1) + 47420065*x + 14580412)/(75*x^3 + 140*x^2 + 87*x + 18)

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Sympy [A]  time = 0.560976, size = 54, normalized size = 0.84 \[ \frac{499350 x^{2} + 615845 x + 189356}{127050 x^{3} + 237160 x^{2} + 147378 x + 30492} - \frac{16 \log{\left (x - \frac{1}{2} \right )}}{65219} + \frac{78475 \log{\left (x + \frac{3}{5} \right )}}{1331} - \frac{2889 \log{\left (x + \frac{2}{3} \right )}}{49} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(499350*x**2 + 615845*x + 189356)/(127050*x**3 + 237160*x**2 + 147378*x + 30492)
- 16*log(x - 1/2)/65219 + 78475*log(x + 3/5)/1331 - 2889*log(x + 2/3)/49

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GIAC/XCAS [A]  time = 0.213267, size = 86, normalized size = 1.34 \[ \frac{27}{7 \,{\left (3 \, x + 2\right )}} - \frac{375 \,{\left (\frac{194}{3 \, x + 2} - 805\right )}}{242 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + \frac{78475}{1331} \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) - \frac{16}{65219} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

27/7/(3*x + 2) - 375/242*(194/(3*x + 2) - 805)/(1/(3*x + 2) - 5)^2 + 78475/1331*
ln(abs(-1/(3*x + 2) + 5)) - 16/65219*ln(abs(-7/(3*x + 2) + 2))