3.1504 \(\int \frac{(2+3 x)^3}{(1-2 x) (3+5 x)^3} \, dx\)

Optimal. Leaf size=43 \[ -\frac{101}{15125 (5 x+3)}-\frac{1}{2750 (5 x+3)^2}-\frac{343 \log (1-2 x)}{2662}+\frac{3469 \log (5 x+3)}{166375} \]

[Out]

-1/(2750*(3 + 5*x)^2) - 101/(15125*(3 + 5*x)) - (343*Log[1 - 2*x])/2662 + (3469*
Log[3 + 5*x])/166375

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Rubi [A]  time = 0.0535047, antiderivative size = 43, 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 \[ -\frac{101}{15125 (5 x+3)}-\frac{1}{2750 (5 x+3)^2}-\frac{343 \log (1-2 x)}{2662}+\frac{3469 \log (5 x+3)}{166375} \]

Antiderivative was successfully verified.

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

[Out]

-1/(2750*(3 + 5*x)^2) - 101/(15125*(3 + 5*x)) - (343*Log[1 - 2*x])/2662 + (3469*
Log[3 + 5*x])/166375

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Rubi in Sympy [A]  time = 7.77685, size = 36, normalized size = 0.84 \[ - \frac{343 \log{\left (- 2 x + 1 \right )}}{2662} + \frac{3469 \log{\left (5 x + 3 \right )}}{166375} - \frac{101}{15125 \left (5 x + 3\right )} - \frac{1}{2750 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-343*log(-2*x + 1)/2662 + 3469*log(5*x + 3)/166375 - 101/(15125*(5*x + 3)) - 1/(
2750*(5*x + 3)**2)

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Mathematica [A]  time = 0.0352682, size = 35, normalized size = 0.81 \[ \frac{-\frac{11 (1010 x+617)}{(5 x+3)^2}-42875 \log (1-2 x)+6938 \log (10 x+6)}{332750} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(617 + 1010*x))/(3 + 5*x)^2 - 42875*Log[1 - 2*x] + 6938*Log[6 + 10*x])/332
750

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Maple [A]  time = 0.011, size = 36, normalized size = 0.8 \[ -{\frac{1}{2750\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{101}{45375+75625\,x}}+{\frac{3469\,\ln \left ( 3+5\,x \right ) }{166375}}-{\frac{343\,\ln \left ( -1+2\,x \right ) }{2662}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2750/(3+5*x)^2-101/15125/(3+5*x)+3469/166375*ln(3+5*x)-343/2662*ln(-1+2*x)

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Maxima [A]  time = 1.3436, size = 49, normalized size = 1.14 \[ -\frac{1010 \, x + 617}{30250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{3469}{166375} \, \log \left (5 \, x + 3\right ) - \frac{343}{2662} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/30250*(1010*x + 617)/(25*x^2 + 30*x + 9) + 3469/166375*log(5*x + 3) - 343/266
2*log(2*x - 1)

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Fricas [A]  time = 0.224466, size = 74, normalized size = 1.72 \[ \frac{6938 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 42875 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 11110 \, x - 6787}{332750 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/332750*(6938*(25*x^2 + 30*x + 9)*log(5*x + 3) - 42875*(25*x^2 + 30*x + 9)*log(
2*x - 1) - 11110*x - 6787)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.414335, size = 34, normalized size = 0.79 \[ - \frac{1010 x + 617}{756250 x^{2} + 907500 x + 272250} - \frac{343 \log{\left (x - \frac{1}{2} \right )}}{2662} + \frac{3469 \log{\left (x + \frac{3}{5} \right )}}{166375} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(1010*x + 617)/(756250*x**2 + 907500*x + 272250) - 343*log(x - 1/2)/2662 + 3469
*log(x + 3/5)/166375

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GIAC/XCAS [A]  time = 0.210103, size = 45, normalized size = 1.05 \[ -\frac{1010 \, x + 617}{30250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{3469}{166375} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{343}{2662} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/30250*(1010*x + 617)/(5*x + 3)^2 + 3469/166375*ln(abs(5*x + 3)) - 343/2662*ln
(abs(2*x - 1))