3.1662 \(\int \frac{1}{(1-2 x)^3 (3+5 x)} \, dx\)

Optimal. Leaf size=43 \[ \frac{5}{121 (1-2 x)}+\frac{1}{22 (1-2 x)^2}-\frac{25 \log (1-2 x)}{1331}+\frac{25 \log (5 x+3)}{1331} \]

[Out]

1/(22*(1 - 2*x)^2) + 5/(121*(1 - 2*x)) - (25*Log[1 - 2*x])/1331 + (25*Log[3 + 5*
x])/1331

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Rubi [A]  time = 0.0349789, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{5}{121 (1-2 x)}+\frac{1}{22 (1-2 x)^2}-\frac{25 \log (1-2 x)}{1331}+\frac{25 \log (5 x+3)}{1331} \]

Antiderivative was successfully verified.

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

[Out]

1/(22*(1 - 2*x)^2) + 5/(121*(1 - 2*x)) - (25*Log[1 - 2*x])/1331 + (25*Log[3 + 5*
x])/1331

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Rubi in Sympy [A]  time = 6.25068, size = 36, normalized size = 0.84 \[ - \frac{25 \log{\left (- 2 x + 1 \right )}}{1331} + \frac{25 \log{\left (5 x + 3 \right )}}{1331} + \frac{5}{121 \left (- 2 x + 1\right )} + \frac{1}{22 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25*log(-2*x + 1)/1331 + 25*log(5*x + 3)/1331 + 5/(121*(-2*x + 1)) + 1/(22*(-2*x
+ 1)**2)

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Mathematica [A]  time = 0.0208357, size = 46, normalized size = 1.07 \[ \frac{-220 x-50 (1-2 x)^2 \log (1-2 x)+50 (1-2 x)^2 \log (10 x+6)+231}{2662 (1-2 x)^2} \]

Antiderivative was successfully verified.

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

[Out]

(231 - 220*x - 50*(1 - 2*x)^2*Log[1 - 2*x] + 50*(1 - 2*x)^2*Log[6 + 10*x])/(2662
*(1 - 2*x)^2)

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Maple [A]  time = 0.01, size = 36, normalized size = 0.8 \[{\frac{25\,\ln \left ( 3+5\,x \right ) }{1331}}+{\frac{1}{22\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{5}{-121+242\,x}}-{\frac{25\,\ln \left ( -1+2\,x \right ) }{1331}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1-2*x)^3/(3+5*x),x)

[Out]

25/1331*ln(3+5*x)+1/22/(-1+2*x)^2-5/121/(-1+2*x)-25/1331*ln(-1+2*x)

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Maxima [A]  time = 1.34628, size = 49, normalized size = 1.14 \[ -\frac{20 \, x - 21}{242 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{25}{1331} \, \log \left (5 \, x + 3\right ) - \frac{25}{1331} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/242*(20*x - 21)/(4*x^2 - 4*x + 1) + 25/1331*log(5*x + 3) - 25/1331*log(2*x -
1)

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Fricas [A]  time = 0.214133, size = 74, normalized size = 1.72 \[ \frac{50 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 50 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 220 \, x + 231}{2662 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2662*(50*(4*x^2 - 4*x + 1)*log(5*x + 3) - 50*(4*x^2 - 4*x + 1)*log(2*x - 1) -
220*x + 231)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.321855, size = 34, normalized size = 0.79 \[ - \frac{20 x - 21}{968 x^{2} - 968 x + 242} - \frac{25 \log{\left (x - \frac{1}{2} \right )}}{1331} + \frac{25 \log{\left (x + \frac{3}{5} \right )}}{1331} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(20*x - 21)/(968*x**2 - 968*x + 242) - 25*log(x - 1/2)/1331 + 25*log(x + 3/5)/1
331

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GIAC/XCAS [A]  time = 0.208737, size = 45, normalized size = 1.05 \[ -\frac{20 \, x - 21}{242 \,{\left (2 \, x - 1\right )}^{2}} + \frac{25}{1331} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{25}{1331} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/242*(20*x - 21)/(2*x - 1)^2 + 25/1331*ln(abs(5*x + 3)) - 25/1331*ln(abs(2*x -
1))