3.1687 \(\int \frac{(2+3 x)^2}{(1-2 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=65 \[ \frac{273}{14641 (1-2 x)}-\frac{72}{14641 (5 x+3)}+\frac{49}{2662 (1-2 x)^2}-\frac{1}{2662 (5 x+3)^2}-\frac{1509 \log (1-2 x)}{161051}+\frac{1509 \log (5 x+3)}{161051} \]

[Out]

49/(2662*(1 - 2*x)^2) + 273/(14641*(1 - 2*x)) - 1/(2662*(3 + 5*x)^2) - 72/(14641
*(3 + 5*x)) - (1509*Log[1 - 2*x])/161051 + (1509*Log[3 + 5*x])/161051

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Rubi [A]  time = 0.0747835, antiderivative size = 65, 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 \[ \frac{273}{14641 (1-2 x)}-\frac{72}{14641 (5 x+3)}+\frac{49}{2662 (1-2 x)^2}-\frac{1}{2662 (5 x+3)^2}-\frac{1509 \log (1-2 x)}{161051}+\frac{1509 \log (5 x+3)}{161051} \]

Antiderivative was successfully verified.

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

[Out]

49/(2662*(1 - 2*x)^2) + 273/(14641*(1 - 2*x)) - 1/(2662*(3 + 5*x)^2) - 72/(14641
*(3 + 5*x)) - (1509*Log[1 - 2*x])/161051 + (1509*Log[3 + 5*x])/161051

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Rubi in Sympy [A]  time = 10.33, size = 53, normalized size = 0.82 \[ - \frac{1509 \log{\left (- 2 x + 1 \right )}}{161051} + \frac{1509 \log{\left (5 x + 3 \right )}}{161051} - \frac{72}{14641 \left (5 x + 3\right )} - \frac{1}{2662 \left (5 x + 3\right )^{2}} + \frac{273}{14641 \left (- 2 x + 1\right )} + \frac{49}{2662 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1509*log(-2*x + 1)/161051 + 1509*log(5*x + 3)/161051 - 72/(14641*(5*x + 3)) - 1
/(2662*(5*x + 3)**2) + 273/(14641*(-2*x + 1)) + 49/(2662*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0493545, size = 48, normalized size = 0.74 \[ \frac{-\frac{11 \left (30180 x^3+4527 x^2-23774 x-9322\right )}{\left (10 x^2+x-3\right )^2}+3018 \log (-5 x-3)-3018 \log (1-2 x)}{322102} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(-9322 - 23774*x + 4527*x^2 + 30180*x^3))/(-3 + x + 10*x^2)^2 + 3018*Log[-
3 - 5*x] - 3018*Log[1 - 2*x])/322102

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Maple [A]  time = 0.019, size = 54, normalized size = 0.8 \[ -{\frac{1}{2662\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{72}{43923+73205\,x}}+{\frac{1509\,\ln \left ( 3+5\,x \right ) }{161051}}+{\frac{49}{2662\, \left ( -1+2\,x \right ) ^{2}}}-{\frac{273}{-14641+29282\,x}}-{\frac{1509\,\ln \left ( -1+2\,x \right ) }{161051}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2662/(3+5*x)^2-72/14641/(3+5*x)+1509/161051*ln(3+5*x)+49/2662/(-1+2*x)^2-273/
14641/(-1+2*x)-1509/161051*ln(-1+2*x)

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Maxima [A]  time = 1.34916, size = 76, normalized size = 1.17 \[ -\frac{30180 \, x^{3} + 4527 \, x^{2} - 23774 \, x - 9322}{29282 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{1509}{161051} \, \log \left (5 \, x + 3\right ) - \frac{1509}{161051} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/29282*(30180*x^3 + 4527*x^2 - 23774*x - 9322)/(100*x^4 + 20*x^3 - 59*x^2 - 6*
x + 9) + 1509/161051*log(5*x + 3) - 1509/161051*log(2*x - 1)

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Fricas [A]  time = 0.209178, size = 128, normalized size = 1.97 \[ -\frac{331980 \, x^{3} + 49797 \, x^{2} - 3018 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 3018 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 261514 \, x - 102542}{322102 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/322102*(331980*x^3 + 49797*x^2 - 3018*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*l
og(5*x + 3) + 3018*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x - 1) - 261514*x
- 102542)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)

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Sympy [A]  time = 0.455779, size = 54, normalized size = 0.83 \[ - \frac{30180 x^{3} + 4527 x^{2} - 23774 x - 9322}{2928200 x^{4} + 585640 x^{3} - 1727638 x^{2} - 175692 x + 263538} - \frac{1509 \log{\left (x - \frac{1}{2} \right )}}{161051} + \frac{1509 \log{\left (x + \frac{3}{5} \right )}}{161051} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(30180*x**3 + 4527*x**2 - 23774*x - 9322)/(2928200*x**4 + 585640*x**3 - 1727638
*x**2 - 175692*x + 263538) - 1509*log(x - 1/2)/161051 + 1509*log(x + 3/5)/161051

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GIAC/XCAS [A]  time = 0.210041, size = 62, normalized size = 0.95 \[ -\frac{30180 \, x^{3} + 4527 \, x^{2} - 23774 \, x - 9322}{29282 \,{\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac{1509}{161051} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{1509}{161051} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/29282*(30180*x^3 + 4527*x^2 - 23774*x - 9322)/(10*x^2 + x - 3)^2 + 1509/16105
1*ln(abs(5*x + 3)) - 1509/161051*ln(abs(2*x - 1))