3.1380 \(\int \frac{(1-2 x)^3}{(2+3 x)^3 (3+5 x)} \, dx\)

Optimal. Leaf size=43 \[ \frac{1421}{27 (3 x+2)}+\frac{343}{54 (3 x+2)^2}-\frac{7189}{27} \log (3 x+2)+\frac{1331}{5} \log (5 x+3) \]

[Out]

343/(54*(2 + 3*x)^2) + 1421/(27*(2 + 3*x)) - (7189*Log[2 + 3*x])/27 + (1331*Log[
3 + 5*x])/5

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Rubi [A]  time = 0.0508837, 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 \[ \frac{1421}{27 (3 x+2)}+\frac{343}{54 (3 x+2)^2}-\frac{7189}{27} \log (3 x+2)+\frac{1331}{5} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(54*(2 + 3*x)^2) + 1421/(27*(2 + 3*x)) - (7189*Log[2 + 3*x])/27 + (1331*Log[
3 + 5*x])/5

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Rubi in Sympy [A]  time = 7.3634, size = 36, normalized size = 0.84 \[ - \frac{7189 \log{\left (3 x + 2 \right )}}{27} + \frac{1331 \log{\left (5 x + 3 \right )}}{5} + \frac{1421}{27 \left (3 x + 2\right )} + \frac{343}{54 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-7189*log(3*x + 2)/27 + 1331*log(5*x + 3)/5 + 1421/(27*(3*x + 2)) + 343/(54*(3*x
+ 2)**2)

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Mathematica [A]  time = 0.0410823, size = 39, normalized size = 0.91 \[ \frac{49 (58 x+41)}{18 (3 x+2)^2}-\frac{7189}{27} \log (5 (3 x+2))+\frac{1331}{5} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(49*(41 + 58*x))/(18*(2 + 3*x)^2) - (7189*Log[5*(2 + 3*x)])/27 + (1331*Log[3 + 5
*x])/5

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Maple [A]  time = 0.011, size = 36, normalized size = 0.8 \[{\frac{343}{54\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{1421}{54+81\,x}}-{\frac{7189\,\ln \left ( 2+3\,x \right ) }{27}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/54/(2+3*x)^2+1421/27/(2+3*x)-7189/27*ln(2+3*x)+1331/5*ln(3+5*x)

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Maxima [A]  time = 1.35044, size = 49, normalized size = 1.14 \[ \frac{49 \,{\left (58 \, x + 41\right )}}{18 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{1331}{5} \, \log \left (5 \, x + 3\right ) - \frac{7189}{27} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/18*(58*x + 41)/(9*x^2 + 12*x + 4) + 1331/5*log(5*x + 3) - 7189/27*log(3*x + 2
)

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Fricas [A]  time = 0.236078, size = 74, normalized size = 1.72 \[ \frac{71874 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 71890 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 42630 \, x + 30135}{270 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/270*(71874*(9*x^2 + 12*x + 4)*log(5*x + 3) - 71890*(9*x^2 + 12*x + 4)*log(3*x
+ 2) + 42630*x + 30135)/(9*x^2 + 12*x + 4)

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Sympy [A]  time = 0.388644, size = 34, normalized size = 0.79 \[ \frac{2842 x + 2009}{162 x^{2} + 216 x + 72} + \frac{1331 \log{\left (x + \frac{3}{5} \right )}}{5} - \frac{7189 \log{\left (x + \frac{2}{3} \right )}}{27} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(2842*x + 2009)/(162*x**2 + 216*x + 72) + 1331*log(x + 3/5)/5 - 7189*log(x + 2/3
)/27

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GIAC/XCAS [A]  time = 0.209856, size = 45, normalized size = 1.05 \[ \frac{49 \,{\left (58 \, x + 41\right )}}{18 \,{\left (3 \, x + 2\right )}^{2}} + \frac{1331}{5} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{7189}{27} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

49/18*(58*x + 41)/(3*x + 2)^2 + 1331/5*ln(abs(5*x + 3)) - 7189/27*ln(abs(3*x + 2
))