3.1591 \(\int \frac{(2+3 x)^3}{(1-2 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=43 \[ \frac{343}{484 (1-2 x)}-\frac{1}{3025 (5 x+3)}+\frac{1421 \log (1-2 x)}{5324}+\frac{103 \log (5 x+3)}{33275} \]

[Out]

343/(484*(1 - 2*x)) - 1/(3025*(3 + 5*x)) + (1421*Log[1 - 2*x])/5324 + (103*Log[3
+ 5*x])/33275

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Rubi [A]  time = 0.0517025, 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 \[ \frac{343}{484 (1-2 x)}-\frac{1}{3025 (5 x+3)}+\frac{1421 \log (1-2 x)}{5324}+\frac{103 \log (5 x+3)}{33275} \]

Antiderivative was successfully verified.

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

[Out]

343/(484*(1 - 2*x)) - 1/(3025*(3 + 5*x)) + (1421*Log[1 - 2*x])/5324 + (103*Log[3
+ 5*x])/33275

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Rubi in Sympy [A]  time = 7.7456, size = 32, normalized size = 0.74 \[ \frac{1421 \log{\left (- 2 x + 1 \right )}}{5324} + \frac{103 \log{\left (5 x + 3 \right )}}{33275} - \frac{1}{3025 \left (5 x + 3\right )} + \frac{343}{484 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1421*log(-2*x + 1)/5324 + 103*log(5*x + 3)/33275 - 1/(3025*(5*x + 3)) + 343/(484
*(-2*x + 1))

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Mathematica [A]  time = 0.035688, size = 40, normalized size = 0.93 \[ \frac{-\frac{11 (42883 x+25721)}{10 x^2+x-3}+35525 \log (3-6 x)+412 \log (-3 (5 x+3))}{133100} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(25721 + 42883*x))/(-3 + x + 10*x^2) + 35525*Log[3 - 6*x] + 412*Log[-3*(3
+ 5*x)])/133100

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Maple [A]  time = 0.014, size = 36, normalized size = 0.8 \[ -{\frac{1}{9075+15125\,x}}+{\frac{103\,\ln \left ( 3+5\,x \right ) }{33275}}-{\frac{343}{-484+968\,x}}+{\frac{1421\,\ln \left ( -1+2\,x \right ) }{5324}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3025/(3+5*x)+103/33275*ln(3+5*x)-343/484/(-1+2*x)+1421/5324*ln(-1+2*x)

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Maxima [A]  time = 1.31818, size = 46, normalized size = 1.07 \[ -\frac{42883 \, x + 25721}{12100 \,{\left (10 \, x^{2} + x - 3\right )}} + \frac{103}{33275} \, \log \left (5 \, x + 3\right ) + \frac{1421}{5324} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/12100*(42883*x + 25721)/(10*x^2 + x - 3) + 103/33275*log(5*x + 3) + 1421/5324
*log(2*x - 1)

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Fricas [A]  time = 0.204399, size = 66, normalized size = 1.53 \[ \frac{412 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 35525 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 471713 \, x - 282931}{133100 \,{\left (10 \, x^{2} + x - 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/133100*(412*(10*x^2 + x - 3)*log(5*x + 3) + 35525*(10*x^2 + x - 3)*log(2*x - 1
) - 471713*x - 282931)/(10*x^2 + x - 3)

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Sympy [A]  time = 0.380029, size = 34, normalized size = 0.79 \[ - \frac{42883 x + 25721}{121000 x^{2} + 12100 x - 36300} + \frac{1421 \log{\left (x - \frac{1}{2} \right )}}{5324} + \frac{103 \log{\left (x + \frac{3}{5} \right )}}{33275} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(42883*x + 25721)/(121000*x**2 + 12100*x - 36300) + 1421*log(x - 1/2)/5324 + 10
3*log(x + 3/5)/33275

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GIAC/XCAS [A]  time = 0.208369, size = 78, normalized size = 1.81 \[ -\frac{1}{3025 \,{\left (5 \, x + 3\right )}} + \frac{1715}{2662 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} - \frac{27}{100} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{1421}{5324} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3025/(5*x + 3) + 1715/2662/(11/(5*x + 3) - 2) - 27/100*ln(1/5*abs(5*x + 3)/(5
*x + 3)^2) + 1421/5324*ln(abs(-11/(5*x + 3) + 2))