3.1284 \(\int \frac{(1-2 x)^2}{(2+3 x)^5 (3+5 x)} \, dx\)

Optimal. Leaf size=59 \[ \frac{605}{3 x+2}+\frac{121}{2 (3 x+2)^2}+\frac{217}{27 (3 x+2)^3}+\frac{49}{36 (3 x+2)^4}-3025 \log (3 x+2)+3025 \log (5 x+3) \]

[Out]

49/(36*(2 + 3*x)^4) + 217/(27*(2 + 3*x)^3) + 121/(2*(2 + 3*x)^2) + 605/(2 + 3*x)
- 3025*Log[2 + 3*x] + 3025*Log[3 + 5*x]

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Rubi [A]  time = 0.065368, antiderivative size = 59, 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 \[ \frac{605}{3 x+2}+\frac{121}{2 (3 x+2)^2}+\frac{217}{27 (3 x+2)^3}+\frac{49}{36 (3 x+2)^4}-3025 \log (3 x+2)+3025 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

49/(36*(2 + 3*x)^4) + 217/(27*(2 + 3*x)^3) + 121/(2*(2 + 3*x)^2) + 605/(2 + 3*x)
- 3025*Log[2 + 3*x] + 3025*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 9.4302, size = 53, normalized size = 0.9 \[ - 3025 \log{\left (3 x + 2 \right )} + 3025 \log{\left (5 x + 3 \right )} + \frac{605}{3 x + 2} + \frac{121}{2 \left (3 x + 2\right )^{2}} + \frac{217}{27 \left (3 x + 2\right )^{3}} + \frac{49}{36 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3025*log(3*x + 2) + 3025*log(5*x + 3) + 605/(3*x + 2) + 121/(2*(3*x + 2)**2) +
217/(27*(3*x + 2)**3) + 49/(36*(3*x + 2)**4)

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Mathematica [A]  time = 0.046331, size = 45, normalized size = 0.76 \[ \frac{1764180 x^3+3587166 x^2+2433252 x+550739}{108 (3 x+2)^4}-3025 \log (5 (3 x+2))+3025 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(550739 + 2433252*x + 3587166*x^2 + 1764180*x^3)/(108*(2 + 3*x)^4) - 3025*Log[5*
(2 + 3*x)] + 3025*Log[3 + 5*x]

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Maple [A]  time = 0.011, size = 54, normalized size = 0.9 \[{\frac{49}{36\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{217}{27\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{121}{2\, \left ( 2+3\,x \right ) ^{2}}}+605\, \left ( 2+3\,x \right ) ^{-1}-3025\,\ln \left ( 2+3\,x \right ) +3025\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/36/(2+3*x)^4+217/27/(2+3*x)^3+121/2/(2+3*x)^2+605/(2+3*x)-3025*ln(2+3*x)+3025
*ln(3+5*x)

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Maxima [A]  time = 1.34368, size = 76, normalized size = 1.29 \[ \frac{1764180 \, x^{3} + 3587166 \, x^{2} + 2433252 \, x + 550739}{108 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + 3025 \, \log \left (5 \, x + 3\right ) - 3025 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/108*(1764180*x^3 + 3587166*x^2 + 2433252*x + 550739)/(81*x^4 + 216*x^3 + 216*x
^2 + 96*x + 16) + 3025*log(5*x + 3) - 3025*log(3*x + 2)

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Fricas [A]  time = 0.216934, size = 128, normalized size = 2.17 \[ \frac{1764180 \, x^{3} + 3587166 \, x^{2} + 326700 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (5 \, x + 3\right ) - 326700 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 2433252 \, x + 550739}{108 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/108*(1764180*x^3 + 3587166*x^2 + 326700*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 1
6)*log(5*x + 3) - 326700*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x + 2) +
2433252*x + 550739)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)

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Sympy [A]  time = 0.498383, size = 51, normalized size = 0.86 \[ \frac{1764180 x^{3} + 3587166 x^{2} + 2433252 x + 550739}{8748 x^{4} + 23328 x^{3} + 23328 x^{2} + 10368 x + 1728} + 3025 \log{\left (x + \frac{3}{5} \right )} - 3025 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(1764180*x**3 + 3587166*x**2 + 2433252*x + 550739)/(8748*x**4 + 23328*x**3 + 233
28*x**2 + 10368*x + 1728) + 3025*log(x + 3/5) - 3025*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.213831, size = 70, normalized size = 1.19 \[ \frac{605}{3 \, x + 2} + \frac{121}{2 \,{\left (3 \, x + 2\right )}^{2}} + \frac{217}{27 \,{\left (3 \, x + 2\right )}^{3}} + \frac{49}{36 \,{\left (3 \, x + 2\right )}^{4}} + 3025 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

605/(3*x + 2) + 121/2/(3*x + 2)^2 + 217/27/(3*x + 2)^3 + 49/36/(3*x + 2)^4 + 302
5*ln(abs(-1/(3*x + 2) + 5))