3.1478 \(\int \frac{1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx\)

Optimal. Leaf size=42 \[ \frac{3}{7 (3 x+2)}-\frac{4}{539} \log (1-2 x)-\frac{111}{49} \log (3 x+2)+\frac{25}{11} \log (5 x+3) \]

[Out]

3/(7*(2 + 3*x)) - (4*Log[1 - 2*x])/539 - (111*Log[2 + 3*x])/49 + (25*Log[3 + 5*x
])/11

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Rubi [A]  time = 0.050652, antiderivative size = 42, 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 \[ \frac{3}{7 (3 x+2)}-\frac{4}{539} \log (1-2 x)-\frac{111}{49} \log (3 x+2)+\frac{25}{11} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

3/(7*(2 + 3*x)) - (4*Log[1 - 2*x])/539 - (111*Log[2 + 3*x])/49 + (25*Log[3 + 5*x
])/11

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Rubi in Sympy [A]  time = 7.49406, size = 36, normalized size = 0.86 \[ - \frac{4 \log{\left (- 2 x + 1 \right )}}{539} - \frac{111 \log{\left (3 x + 2 \right )}}{49} + \frac{25 \log{\left (5 x + 3 \right )}}{11} + \frac{3}{7 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-4*log(-2*x + 1)/539 - 111*log(3*x + 2)/49 + 25*log(5*x + 3)/11 + 3/(7*(3*x + 2)
)

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Mathematica [A]  time = 0.0328795, size = 38, normalized size = 0.9 \[ \frac{1}{539} \left (\frac{231}{3 x+2}-4 \log (1-2 x)-1221 \log (6 x+4)+1225 \log (10 x+6)\right ) \]

Antiderivative was successfully verified.

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

[Out]

(231/(2 + 3*x) - 4*Log[1 - 2*x] - 1221*Log[4 + 6*x] + 1225*Log[6 + 10*x])/539

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Maple [A]  time = 0.013, size = 35, normalized size = 0.8 \[{\frac{25\,\ln \left ( 3+5\,x \right ) }{11}}+{\frac{3}{14+21\,x}}-{\frac{111\,\ln \left ( 2+3\,x \right ) }{49}}-{\frac{4\,\ln \left ( -1+2\,x \right ) }{539}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25/11*ln(3+5*x)+3/7/(2+3*x)-111/49*ln(2+3*x)-4/539*ln(-1+2*x)

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Maxima [A]  time = 1.343, size = 46, normalized size = 1.1 \[ \frac{3}{7 \,{\left (3 \, x + 2\right )}} + \frac{25}{11} \, \log \left (5 \, x + 3\right ) - \frac{111}{49} \, \log \left (3 \, x + 2\right ) - \frac{4}{539} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/7/(3*x + 2) + 25/11*log(5*x + 3) - 111/49*log(3*x + 2) - 4/539*log(2*x - 1)

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Fricas [A]  time = 0.220606, size = 68, normalized size = 1.62 \[ \frac{1225 \,{\left (3 \, x + 2\right )} \log \left (5 \, x + 3\right ) - 1221 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 4 \,{\left (3 \, x + 2\right )} \log \left (2 \, x - 1\right ) + 231}{539 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/539*(1225*(3*x + 2)*log(5*x + 3) - 1221*(3*x + 2)*log(3*x + 2) - 4*(3*x + 2)*l
og(2*x - 1) + 231)/(3*x + 2)

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Sympy [A]  time = 0.413513, size = 36, normalized size = 0.86 \[ - \frac{4 \log{\left (x - \frac{1}{2} \right )}}{539} + \frac{25 \log{\left (x + \frac{3}{5} \right )}}{11} - \frac{111 \log{\left (x + \frac{2}{3} \right )}}{49} + \frac{3}{21 x + 14} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-4*log(x - 1/2)/539 + 25*log(x + 3/5)/11 - 111*log(x + 2/3)/49 + 3/(21*x + 14)

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GIAC/XCAS [A]  time = 0.209265, size = 54, normalized size = 1.29 \[ \frac{3}{7 \,{\left (3 \, x + 2\right )}} + \frac{25}{11} \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) - \frac{4}{539} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/7/(3*x + 2) + 25/11*ln(abs(-1/(3*x + 2) + 5)) - 4/539*ln(abs(-7/(3*x + 2) + 2)
)