3.1565 \(\int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)^3} \, dx\)

Optimal. Leaf size=54 \[ \frac{1331}{686 (1-2 x)}-\frac{101}{3087 (3 x+2)}+\frac{1}{882 (3 x+2)^2}+\frac{363 \log (1-2 x)}{2401}-\frac{363 \log (3 x+2)}{2401} \]

[Out]

1331/(686*(1 - 2*x)) + 1/(882*(2 + 3*x)^2) - 101/(3087*(2 + 3*x)) + (363*Log[1 -
2*x])/2401 - (363*Log[2 + 3*x])/2401

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Rubi [A]  time = 0.0639553, antiderivative size = 54, 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 \[ \frac{1331}{686 (1-2 x)}-\frac{101}{3087 (3 x+2)}+\frac{1}{882 (3 x+2)^2}+\frac{363 \log (1-2 x)}{2401}-\frac{363 \log (3 x+2)}{2401} \]

Antiderivative was successfully verified.

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

[Out]

1331/(686*(1 - 2*x)) + 1/(882*(2 + 3*x)^2) - 101/(3087*(2 + 3*x)) + (363*Log[1 -
2*x])/2401 - (363*Log[2 + 3*x])/2401

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Rubi in Sympy [A]  time = 9.01275, size = 42, normalized size = 0.78 \[ \frac{363 \log{\left (- 2 x + 1 \right )}}{2401} - \frac{363 \log{\left (3 x + 2 \right )}}{2401} - \frac{101}{3087 \left (3 x + 2\right )} + \frac{1}{882 \left (3 x + 2\right )^{2}} + \frac{1331}{686 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

363*log(-2*x + 1)/2401 - 363*log(3*x + 2)/2401 - 101/(3087*(3*x + 2)) + 1/(882*(
3*x + 2)**2) + 1331/(686*(-2*x + 1))

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Mathematica [A]  time = 0.0521153, size = 48, normalized size = 0.89 \[ \frac{\frac{83853}{1-2 x}-\frac{1414}{3 x+2}+\frac{49}{(3 x+2)^2}+6534 \log (1-2 x)-6534 \log (6 x+4)}{43218} \]

Antiderivative was successfully verified.

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

[Out]

(83853/(1 - 2*x) + 49/(2 + 3*x)^2 - 1414/(2 + 3*x) + 6534*Log[1 - 2*x] - 6534*Lo
g[4 + 6*x])/43218

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Maple [A]  time = 0.014, size = 45, normalized size = 0.8 \[{\frac{1}{882\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{101}{6174+9261\,x}}-{\frac{363\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{1331}{-686+1372\,x}}+{\frac{363\,\ln \left ( -1+2\,x \right ) }{2401}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/882/(2+3*x)^2-101/3087/(2+3*x)-363/2401*ln(2+3*x)-1331/686/(-1+2*x)+363/2401*l
n(-1+2*x)

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Maxima [A]  time = 1.34473, size = 62, normalized size = 1.15 \[ -\frac{109023 \, x^{2} + 143936 \, x + 47519}{6174 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} - \frac{363}{2401} \, \log \left (3 \, x + 2\right ) + \frac{363}{2401} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6174*(109023*x^2 + 143936*x + 47519)/(18*x^3 + 15*x^2 - 4*x - 4) - 363/2401*l
og(3*x + 2) + 363/2401*log(2*x - 1)

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Fricas [A]  time = 0.208436, size = 101, normalized size = 1.87 \[ -\frac{763161 \, x^{2} + 6534 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (3 \, x + 2\right ) - 6534 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (2 \, x - 1\right ) + 1007552 \, x + 332633}{43218 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/43218*(763161*x^2 + 6534*(18*x^3 + 15*x^2 - 4*x - 4)*log(3*x + 2) - 6534*(18*
x^3 + 15*x^2 - 4*x - 4)*log(2*x - 1) + 1007552*x + 332633)/(18*x^3 + 15*x^2 - 4*
x - 4)

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Sympy [A]  time = 0.394536, size = 44, normalized size = 0.81 \[ - \frac{109023 x^{2} + 143936 x + 47519}{111132 x^{3} + 92610 x^{2} - 24696 x - 24696} + \frac{363 \log{\left (x - \frac{1}{2} \right )}}{2401} - \frac{363 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(109023*x**2 + 143936*x + 47519)/(111132*x**3 + 92610*x**2 - 24696*x - 24696) +
363*log(x - 1/2)/2401 - 363*log(x + 2/3)/2401

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GIAC/XCAS [A]  time = 0.207849, size = 69, normalized size = 1.28 \[ -\frac{1331}{686 \,{\left (2 \, x - 1\right )}} + \frac{2 \,{\left (\frac{231}{2 \, x - 1} + 100\right )}}{2401 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{2}} - \frac{363}{2401} \,{\rm ln}\left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1331/686/(2*x - 1) + 2/2401*(231/(2*x - 1) + 100)/(7/(2*x - 1) + 3)^2 - 363/240
1*ln(abs(-7/(2*x - 1) - 3))