3.1480 \(\int \frac{1}{(1-2 x) (2+3 x)^4 (3+5 x)} \, dx\)

Optimal. Leaf size=64 \[ \frac{3897}{343 (3 x+2)}+\frac{111}{98 (3 x+2)^2}+\frac{1}{7 (3 x+2)^3}-\frac{16 \log (1-2 x)}{26411}-\frac{136419 \log (3 x+2)}{2401}+\frac{625}{11} \log (5 x+3) \]

[Out]

1/(7*(2 + 3*x)^3) + 111/(98*(2 + 3*x)^2) + 3897/(343*(2 + 3*x)) - (16*Log[1 - 2*
x])/26411 - (136419*Log[2 + 3*x])/2401 + (625*Log[3 + 5*x])/11

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Rubi [A]  time = 0.0710004, antiderivative size = 64, 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 \[ \frac{3897}{343 (3 x+2)}+\frac{111}{98 (3 x+2)^2}+\frac{1}{7 (3 x+2)^3}-\frac{16 \log (1-2 x)}{26411}-\frac{136419 \log (3 x+2)}{2401}+\frac{625}{11} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)),x]

[Out]

1/(7*(2 + 3*x)^3) + 111/(98*(2 + 3*x)^2) + 3897/(343*(2 + 3*x)) - (16*Log[1 - 2*
x])/26411 - (136419*Log[2 + 3*x])/2401 + (625*Log[3 + 5*x])/11

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Rubi in Sympy [A]  time = 10.0042, size = 56, normalized size = 0.88 \[ - \frac{16 \log{\left (- 2 x + 1 \right )}}{26411} - \frac{136419 \log{\left (3 x + 2 \right )}}{2401} + \frac{625 \log{\left (5 x + 3 \right )}}{11} + \frac{3897}{343 \left (3 x + 2\right )} + \frac{111}{98 \left (3 x + 2\right )^{2}} + \frac{1}{7 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(1-2*x)/(2+3*x)**4/(3+5*x),x)

[Out]

-16*log(-2*x + 1)/26411 - 136419*log(3*x + 2)/2401 + 625*log(5*x + 3)/11 + 3897/
(343*(3*x + 2)) + 111/(98*(3*x + 2)**2) + 1/(7*(3*x + 2)**3)

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Mathematica [A]  time = 0.0799657, size = 50, normalized size = 0.78 \[ \frac{\frac{77 \left (70146 x^2+95859 x+32828\right )}{2 (3 x+2)^3}-16 \log (1-2 x)-1500609 \log (6 x+4)+1500625 \log (10 x+6)}{26411} \]

Antiderivative was successfully verified.

[In]  Integrate[1/((1 - 2*x)*(2 + 3*x)^4*(3 + 5*x)),x]

[Out]

((77*(32828 + 95859*x + 70146*x^2))/(2*(2 + 3*x)^3) - 16*Log[1 - 2*x] - 1500609*
Log[4 + 6*x] + 1500625*Log[6 + 10*x])/26411

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Maple [A]  time = 0.014, size = 53, normalized size = 0.8 \[{\frac{625\,\ln \left ( 3+5\,x \right ) }{11}}+{\frac{1}{7\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{111}{98\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{3897}{686+1029\,x}}-{\frac{136419\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{16\,\ln \left ( -1+2\,x \right ) }{26411}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(1-2*x)/(2+3*x)^4/(3+5*x),x)

[Out]

625/11*ln(3+5*x)+1/7/(2+3*x)^3+111/98/(2+3*x)^2+3897/343/(2+3*x)-136419/2401*ln(
2+3*x)-16/26411*ln(-1+2*x)

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Maxima [A]  time = 1.34475, size = 73, normalized size = 1.14 \[ \frac{70146 \, x^{2} + 95859 \, x + 32828}{686 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{625}{11} \, \log \left (5 \, x + 3\right ) - \frac{136419}{2401} \, \log \left (3 \, x + 2\right ) - \frac{16}{26411} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)),x, algorithm="maxima")

[Out]

1/686*(70146*x^2 + 95859*x + 32828)/(27*x^3 + 54*x^2 + 36*x + 8) + 625/11*log(5*
x + 3) - 136419/2401*log(3*x + 2) - 16/26411*log(2*x - 1)

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Fricas [A]  time = 0.220139, size = 132, normalized size = 2.06 \[ \frac{5401242 \, x^{2} + 3001250 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 3001218 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 32 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (2 \, x - 1\right ) + 7381143 \, x + 2527756}{52822 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)),x, algorithm="fricas")

[Out]

1/52822*(5401242*x^2 + 3001250*(27*x^3 + 54*x^2 + 36*x + 8)*log(5*x + 3) - 30012
18*(27*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) - 32*(27*x^3 + 54*x^2 + 36*x + 8)*l
og(2*x - 1) + 7381143*x + 2527756)/(27*x^3 + 54*x^2 + 36*x + 8)

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Sympy [A]  time = 0.555386, size = 54, normalized size = 0.84 \[ \frac{70146 x^{2} + 95859 x + 32828}{18522 x^{3} + 37044 x^{2} + 24696 x + 5488} - \frac{16 \log{\left (x - \frac{1}{2} \right )}}{26411} + \frac{625 \log{\left (x + \frac{3}{5} \right )}}{11} - \frac{136419 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(1-2*x)/(2+3*x)**4/(3+5*x),x)

[Out]

(70146*x**2 + 95859*x + 32828)/(18522*x**3 + 37044*x**2 + 24696*x + 5488) - 16*l
og(x - 1/2)/26411 + 625*log(x + 3/5)/11 - 136419*log(x + 2/3)/2401

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GIAC/XCAS [A]  time = 0.215064, size = 63, normalized size = 0.98 \[ \frac{70146 \, x^{2} + 95859 \, x + 32828}{686 \,{\left (3 \, x + 2\right )}^{3}} + \frac{625}{11} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{136419}{2401} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) - \frac{16}{26411} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-1/((5*x + 3)*(3*x + 2)^4*(2*x - 1)),x, algorithm="giac")

[Out]

1/686*(70146*x^2 + 95859*x + 32828)/(3*x + 2)^3 + 625/11*ln(abs(5*x + 3)) - 1364
19/2401*ln(abs(3*x + 2)) - 16/26411*ln(abs(2*x - 1))