3.1283 \(\int \frac{(1-2 x)^2}{(2+3 x)^4 (3+5 x)} \, dx\)

Optimal. Leaf size=48 \[ \frac{121}{3 x+2}+\frac{217}{18 (3 x+2)^2}+\frac{49}{27 (3 x+2)^3}-605 \log (3 x+2)+605 \log (5 x+3) \]

[Out]

49/(27*(2 + 3*x)^3) + 217/(18*(2 + 3*x)^2) + 121/(2 + 3*x) - 605*Log[2 + 3*x] +
605*Log[3 + 5*x]

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Rubi [A]  time = 0.0552137, antiderivative size = 48, 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 \[ \frac{121}{3 x+2}+\frac{217}{18 (3 x+2)^2}+\frac{49}{27 (3 x+2)^3}-605 \log (3 x+2)+605 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

49/(27*(2 + 3*x)^3) + 217/(18*(2 + 3*x)^2) + 121/(2 + 3*x) - 605*Log[2 + 3*x] +
605*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 8.32102, size = 42, normalized size = 0.88 \[ - 605 \log{\left (3 x + 2 \right )} + 605 \log{\left (5 x + 3 \right )} + \frac{121}{3 x + 2} + \frac{217}{18 \left (3 x + 2\right )^{2}} + \frac{49}{27 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-605*log(3*x + 2) + 605*log(5*x + 3) + 121/(3*x + 2) + 217/(18*(3*x + 2)**2) + 4
9/(27*(3*x + 2)**3)

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Mathematica [A]  time = 0.0439673, size = 40, normalized size = 0.83 \[ \frac{58806 x^2+80361 x+27536}{54 (3 x+2)^3}-605 \log (5 (3 x+2))+605 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(27536 + 80361*x + 58806*x^2)/(54*(2 + 3*x)^3) - 605*Log[5*(2 + 3*x)] + 605*Log[
3 + 5*x]

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Maple [A]  time = 0.01, size = 45, normalized size = 0.9 \[{\frac{49}{27\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{217}{18\, \left ( 2+3\,x \right ) ^{2}}}+121\, \left ( 2+3\,x \right ) ^{-1}-605\,\ln \left ( 2+3\,x \right ) +605\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/27/(2+3*x)^3+217/18/(2+3*x)^2+121/(2+3*x)-605*ln(2+3*x)+605*ln(3+5*x)

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Maxima [A]  time = 1.34481, size = 62, normalized size = 1.29 \[ \frac{58806 \, x^{2} + 80361 \, x + 27536}{54 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + 605 \, \log \left (5 \, x + 3\right ) - 605 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/54*(58806*x^2 + 80361*x + 27536)/(27*x^3 + 54*x^2 + 36*x + 8) + 605*log(5*x +
3) - 605*log(3*x + 2)

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Fricas [A]  time = 0.212192, size = 101, normalized size = 2.1 \[ \frac{58806 \, x^{2} + 32670 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 32670 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 80361 \, x + 27536}{54 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/54*(58806*x^2 + 32670*(27*x^3 + 54*x^2 + 36*x + 8)*log(5*x + 3) - 32670*(27*x^
3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 80361*x + 27536)/(27*x^3 + 54*x^2 + 36*x +
8)

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Sympy [A]  time = 0.376095, size = 41, normalized size = 0.85 \[ \frac{58806 x^{2} + 80361 x + 27536}{1458 x^{3} + 2916 x^{2} + 1944 x + 432} + 605 \log{\left (x + \frac{3}{5} \right )} - 605 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(58806*x**2 + 80361*x + 27536)/(1458*x**3 + 2916*x**2 + 1944*x + 432) + 605*log(
x + 3/5) - 605*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.235742, size = 51, normalized size = 1.06 \[ \frac{58806 \, x^{2} + 80361 \, x + 27536}{54 \,{\left (3 \, x + 2\right )}^{3}} + 605 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 605 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/54*(58806*x^2 + 80361*x + 27536)/(3*x + 2)^3 + 605*ln(abs(5*x + 3)) - 605*ln(a
bs(3*x + 2))