3.1663 \(\int \frac{1}{(1-2 x)^3 (2+3 x) (3+5 x)} \, dx\)

Optimal. Leaf size=53 \[ \frac{136}{5929 (1-2 x)}+\frac{1}{77 (1-2 x)^2}-\frac{6938 \log (1-2 x)}{456533}-\frac{27}{343} \log (3 x+2)+\frac{125 \log (5 x+3)}{1331} \]

[Out]

1/(77*(1 - 2*x)^2) + 136/(5929*(1 - 2*x)) - (6938*Log[1 - 2*x])/456533 - (27*Log
[2 + 3*x])/343 + (125*Log[3 + 5*x])/1331

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Rubi [A]  time = 0.0617132, antiderivative size = 53, 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 \[ \frac{136}{5929 (1-2 x)}+\frac{1}{77 (1-2 x)^2}-\frac{6938 \log (1-2 x)}{456533}-\frac{27}{343} \log (3 x+2)+\frac{125 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

1/(77*(1 - 2*x)^2) + 136/(5929*(1 - 2*x)) - (6938*Log[1 - 2*x])/456533 - (27*Log
[2 + 3*x])/343 + (125*Log[3 + 5*x])/1331

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Rubi in Sympy [A]  time = 8.71225, size = 46, normalized size = 0.87 \[ - \frac{6938 \log{\left (- 2 x + 1 \right )}}{456533} - \frac{27 \log{\left (3 x + 2 \right )}}{343} + \frac{125 \log{\left (5 x + 3 \right )}}{1331} + \frac{136}{5929 \left (- 2 x + 1\right )} + \frac{1}{77 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6938*log(-2*x + 1)/456533 - 27*log(3*x + 2)/343 + 125*log(5*x + 3)/1331 + 136/(
5929*(-2*x + 1)) + 1/(77*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0458772, size = 52, normalized size = 0.98 \[ \frac{-6938 \log (3-6 x)-35937 \log (3 x+2)+\frac{7 \left (-2992 x+6125 (1-2 x)^2 \log (-3 (5 x+3))+2343\right )}{(1-2 x)^2}}{456533} \]

Antiderivative was successfully verified.

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

[Out]

(-6938*Log[3 - 6*x] - 35937*Log[2 + 3*x] + (7*(2343 - 2992*x + 6125*(1 - 2*x)^2*
Log[-3*(3 + 5*x)]))/(1 - 2*x)^2)/456533

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Maple [A]  time = 0.015, size = 44, normalized size = 0.8 \[{\frac{125\,\ln \left ( 3+5\,x \right ) }{1331}}-{\frac{27\,\ln \left ( 2+3\,x \right ) }{343}}+{\frac{1}{77\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{136}{-5929+11858\,x}}-{\frac{6938\,\ln \left ( -1+2\,x \right ) }{456533}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/1331*ln(3+5*x)-27/343*ln(2+3*x)+1/77/(-1+2*x)^2-136/5929/(-1+2*x)-6938/45653
3*ln(-1+2*x)

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Maxima [A]  time = 1.35296, size = 59, normalized size = 1.11 \[ -\frac{272 \, x - 213}{5929 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{125}{1331} \, \log \left (5 \, x + 3\right ) - \frac{27}{343} \, \log \left (3 \, x + 2\right ) - \frac{6938}{456533} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/5929*(272*x - 213)/(4*x^2 - 4*x + 1) + 125/1331*log(5*x + 3) - 27/343*log(3*x
+ 2) - 6938/456533*log(2*x - 1)

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Fricas [A]  time = 0.210698, size = 99, normalized size = 1.87 \[ \frac{42875 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 35937 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) - 6938 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 20944 \, x + 16401}{456533 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/456533*(42875*(4*x^2 - 4*x + 1)*log(5*x + 3) - 35937*(4*x^2 - 4*x + 1)*log(3*x
+ 2) - 6938*(4*x^2 - 4*x + 1)*log(2*x - 1) - 20944*x + 16401)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.49509, size = 44, normalized size = 0.83 \[ - \frac{272 x - 213}{23716 x^{2} - 23716 x + 5929} - \frac{6938 \log{\left (x - \frac{1}{2} \right )}}{456533} + \frac{125 \log{\left (x + \frac{3}{5} \right )}}{1331} - \frac{27 \log{\left (x + \frac{2}{3} \right )}}{343} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(272*x - 213)/(23716*x**2 - 23716*x + 5929) - 6938*log(x - 1/2)/456533 + 125*lo
g(x + 3/5)/1331 - 27*log(x + 2/3)/343

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GIAC/XCAS [A]  time = 0.216307, size = 57, normalized size = 1.08 \[ -\frac{272 \, x - 213}{5929 \,{\left (2 \, x - 1\right )}^{2}} + \frac{125}{1331} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{27}{343} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{6938}{456533} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/5929*(272*x - 213)/(2*x - 1)^2 + 125/1331*ln(abs(5*x + 3)) - 27/343*ln(abs(3*
x + 2)) - 6938/456533*ln(abs(2*x - 1))