3.1479 \(\int \frac{1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx\)

Optimal. Leaf size=53 \[ \frac{111}{49 (3 x+2)}+\frac{3}{14 (3 x+2)^2}-\frac{8 \log (1-2 x)}{3773}-\frac{3897}{343} \log (3 x+2)+\frac{125}{11} \log (5 x+3) \]

[Out]

3/(14*(2 + 3*x)^2) + 111/(49*(2 + 3*x)) - (8*Log[1 - 2*x])/3773 - (3897*Log[2 +
3*x])/343 + (125*Log[3 + 5*x])/11

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Rubi [A]  time = 0.0624703, 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 \[ \frac{111}{49 (3 x+2)}+\frac{3}{14 (3 x+2)^2}-\frac{8 \log (1-2 x)}{3773}-\frac{3897}{343} \log (3 x+2)+\frac{125}{11} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

3/(14*(2 + 3*x)^2) + 111/(49*(2 + 3*x)) - (8*Log[1 - 2*x])/3773 - (3897*Log[2 +
3*x])/343 + (125*Log[3 + 5*x])/11

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Rubi in Sympy [A]  time = 8.72003, size = 46, normalized size = 0.87 \[ - \frac{8 \log{\left (- 2 x + 1 \right )}}{3773} - \frac{3897 \log{\left (3 x + 2 \right )}}{343} + \frac{125 \log{\left (5 x + 3 \right )}}{11} + \frac{111}{49 \left (3 x + 2\right )} + \frac{3}{14 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*log(-2*x + 1)/3773 - 3897*log(3*x + 2)/343 + 125*log(5*x + 3)/11 + 111/(49*(3
*x + 2)) + 3/(14*(3*x + 2)**2)

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Mathematica [A]  time = 0.0354109, size = 49, normalized size = 0.92 \[ \frac{\frac{8547}{3 x+2}+\frac{1617}{2 (3 x+2)^2}-8 \log (1-2 x)-42867 \log (6 x+4)+42875 \log (10 x+6)}{3773} \]

Antiderivative was successfully verified.

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

[Out]

(1617/(2*(2 + 3*x)^2) + 8547/(2 + 3*x) - 8*Log[1 - 2*x] - 42867*Log[4 + 6*x] + 4
2875*Log[6 + 10*x])/3773

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Maple [A]  time = 0.013, size = 44, normalized size = 0.8 \[{\frac{125\,\ln \left ( 3+5\,x \right ) }{11}}+{\frac{3}{14\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{111}{98+147\,x}}-{\frac{3897\,\ln \left ( 2+3\,x \right ) }{343}}-{\frac{8\,\ln \left ( -1+2\,x \right ) }{3773}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/11*ln(3+5*x)+3/14/(2+3*x)^2+111/49/(2+3*x)-3897/343*ln(2+3*x)-8/3773*ln(-1+2
*x)

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Maxima [A]  time = 1.35418, size = 59, normalized size = 1.11 \[ \frac{3 \,{\left (222 \, x + 155\right )}}{98 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{125}{11} \, \log \left (5 \, x + 3\right ) - \frac{3897}{343} \, \log \left (3 \, x + 2\right ) - \frac{8}{3773} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/98*(222*x + 155)/(9*x^2 + 12*x + 4) + 125/11*log(5*x + 3) - 3897/343*log(3*x +
2) - 8/3773*log(2*x - 1)

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Fricas [A]  time = 0.217574, size = 99, normalized size = 1.87 \[ \frac{85750 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 85734 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 16 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (2 \, x - 1\right ) + 51282 \, x + 35805}{7546 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7546*(85750*(9*x^2 + 12*x + 4)*log(5*x + 3) - 85734*(9*x^2 + 12*x + 4)*log(3*x
+ 2) - 16*(9*x^2 + 12*x + 4)*log(2*x - 1) + 51282*x + 35805)/(9*x^2 + 12*x + 4)

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Sympy [A]  time = 0.487871, size = 44, normalized size = 0.83 \[ \frac{666 x + 465}{882 x^{2} + 1176 x + 392} - \frac{8 \log{\left (x - \frac{1}{2} \right )}}{3773} + \frac{125 \log{\left (x + \frac{3}{5} \right )}}{11} - \frac{3897 \log{\left (x + \frac{2}{3} \right )}}{343} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(666*x + 465)/(882*x**2 + 1176*x + 392) - 8*log(x - 1/2)/3773 + 125*log(x + 3/5)
/11 - 3897*log(x + 2/3)/343

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GIAC/XCAS [A]  time = 0.213433, size = 57, normalized size = 1.08 \[ \frac{3 \,{\left (222 \, x + 155\right )}}{98 \,{\left (3 \, x + 2\right )}^{2}} + \frac{125}{11} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{3897}{343} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{8}{3773} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/98*(222*x + 155)/(3*x + 2)^2 + 125/11*ln(abs(5*x + 3)) - 3897/343*ln(abs(3*x +
2)) - 8/3773*ln(abs(2*x - 1))