3.1382 \(\int \frac{(1-2 x)^3}{(2+3 x)^5 (3+5 x)} \, dx\)

Optimal. Leaf size=59 \[ \frac{1331}{3 x+2}+\frac{7189}{54 (3 x+2)^2}+\frac{1421}{81 (3 x+2)^3}+\frac{343}{108 (3 x+2)^4}-6655 \log (3 x+2)+6655 \log (5 x+3) \]

[Out]

343/(108*(2 + 3*x)^4) + 1421/(81*(2 + 3*x)^3) + 7189/(54*(2 + 3*x)^2) + 1331/(2
+ 3*x) - 6655*Log[2 + 3*x] + 6655*Log[3 + 5*x]

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Rubi [A]  time = 0.0645662, 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 \[ \frac{1331}{3 x+2}+\frac{7189}{54 (3 x+2)^2}+\frac{1421}{81 (3 x+2)^3}+\frac{343}{108 (3 x+2)^4}-6655 \log (3 x+2)+6655 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(108*(2 + 3*x)^4) + 1421/(81*(2 + 3*x)^3) + 7189/(54*(2 + 3*x)^2) + 1331/(2
+ 3*x) - 6655*Log[2 + 3*x] + 6655*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 9.40213, size = 53, normalized size = 0.9 \[ - 6655 \log{\left (3 x + 2 \right )} + 6655 \log{\left (5 x + 3 \right )} + \frac{1331}{3 x + 2} + \frac{7189}{54 \left (3 x + 2\right )^{2}} + \frac{1421}{81 \left (3 x + 2\right )^{3}} + \frac{343}{108 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6655*log(3*x + 2) + 6655*log(5*x + 3) + 1331/(3*x + 2) + 7189/(54*(3*x + 2)**2)
+ 1421/(81*(3*x + 2)**3) + 343/(108*(3*x + 2)**4)

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Mathematica [A]  time = 0.0483789, size = 45, normalized size = 0.76 \[ \frac{11643588 x^3+23675382 x^2+16059444 x+3634885}{324 (3 x+2)^4}-6655 \log (5 (3 x+2))+6655 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(3634885 + 16059444*x + 23675382*x^2 + 11643588*x^3)/(324*(2 + 3*x)^4) - 6655*Lo
g[5*(2 + 3*x)] + 6655*Log[3 + 5*x]

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Maple [A]  time = 0.013, size = 54, normalized size = 0.9 \[{\frac{343}{108\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{1421}{81\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{7189}{54\, \left ( 2+3\,x \right ) ^{2}}}+1331\, \left ( 2+3\,x \right ) ^{-1}-6655\,\ln \left ( 2+3\,x \right ) +6655\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/108/(2+3*x)^4+1421/81/(2+3*x)^3+7189/54/(2+3*x)^2+1331/(2+3*x)-6655*ln(2+3*x
)+6655*ln(3+5*x)

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Maxima [A]  time = 1.3472, size = 76, normalized size = 1.29 \[ \frac{11643588 \, x^{3} + 23675382 \, x^{2} + 16059444 \, x + 3634885}{324 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + 6655 \, \log \left (5 \, x + 3\right ) - 6655 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/324*(11643588*x^3 + 23675382*x^2 + 16059444*x + 3634885)/(81*x^4 + 216*x^3 + 2
16*x^2 + 96*x + 16) + 6655*log(5*x + 3) - 6655*log(3*x + 2)

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Fricas [A]  time = 0.215106, size = 128, normalized size = 2.17 \[ \frac{11643588 \, x^{3} + 23675382 \, x^{2} + 2156220 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (5 \, x + 3\right ) - 2156220 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 16059444 \, x + 3634885}{324 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/324*(11643588*x^3 + 23675382*x^2 + 2156220*(81*x^4 + 216*x^3 + 216*x^2 + 96*x
+ 16)*log(5*x + 3) - 2156220*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(3*x +
2) + 16059444*x + 3634885)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)

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Sympy [A]  time = 0.44264, size = 51, normalized size = 0.86 \[ \frac{11643588 x^{3} + 23675382 x^{2} + 16059444 x + 3634885}{26244 x^{4} + 69984 x^{3} + 69984 x^{2} + 31104 x + 5184} + 6655 \log{\left (x + \frac{3}{5} \right )} - 6655 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(11643588*x**3 + 23675382*x**2 + 16059444*x + 3634885)/(26244*x**4 + 69984*x**3
+ 69984*x**2 + 31104*x + 5184) + 6655*log(x + 3/5) - 6655*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.217765, size = 70, normalized size = 1.19 \[ \frac{1331}{3 \, x + 2} + \frac{7189}{54 \,{\left (3 \, x + 2\right )}^{2}} + \frac{1421}{81 \,{\left (3 \, x + 2\right )}^{3}} + \frac{343}{108 \,{\left (3 \, x + 2\right )}^{4}} + 6655 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1331/(3*x + 2) + 7189/54/(3*x + 2)^2 + 1421/81/(3*x + 2)^3 + 343/108/(3*x + 2)^4
+ 6655*ln(abs(-1/(3*x + 2) + 5))