3.1410 \(\int \frac{(1-2 x)^3}{(2+3 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=50 \[ \frac{343}{3 (3 x+2)}+\frac{8712}{25 (5 x+3)}-\frac{1331}{50 (5 x+3)^2}-1617 \log (3 x+2)+1617 \log (5 x+3) \]

[Out]

343/(3*(2 + 3*x)) - 1331/(50*(3 + 5*x)^2) + 8712/(25*(3 + 5*x)) - 1617*Log[2 + 3
*x] + 1617*Log[3 + 5*x]

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Rubi [A]  time = 0.0622917, antiderivative size = 50, 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 \[ \frac{343}{3 (3 x+2)}+\frac{8712}{25 (5 x+3)}-\frac{1331}{50 (5 x+3)^2}-1617 \log (3 x+2)+1617 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(3*(2 + 3*x)) - 1331/(50*(3 + 5*x)^2) + 8712/(25*(3 + 5*x)) - 1617*Log[2 + 3
*x] + 1617*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 8.48222, size = 39, normalized size = 0.78 \[ - 1617 \log{\left (3 x + 2 \right )} + 1617 \log{\left (5 x + 3 \right )} + \frac{8712}{25 \left (5 x + 3\right )} - \frac{1331}{50 \left (5 x + 3\right )^{2}} + \frac{343}{3 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1617*log(3*x + 2) + 1617*log(5*x + 3) + 8712/(25*(5*x + 3)) - 1331/(50*(5*x + 3
)**2) + 343/(3*(3*x + 2))

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Mathematica [A]  time = 0.0457259, size = 48, normalized size = 0.96 \[ \frac{343}{9 x+6}+\frac{8712}{125 x+75}-\frac{1331}{50 (5 x+3)^2}-1617 \log (5 (3 x+2))+1617 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-1331/(50*(3 + 5*x)^2) + 343/(6 + 9*x) + 8712/(75 + 125*x) - 1617*Log[5*(2 + 3*x
)] + 1617*Log[3 + 5*x]

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Maple [A]  time = 0.014, size = 45, normalized size = 0.9 \[{\frac{343}{6+9\,x}}-{\frac{1331}{50\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{8712}{75+125\,x}}-1617\,\ln \left ( 2+3\,x \right ) +1617\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/3/(2+3*x)-1331/50/(3+5*x)^2+8712/25/(3+5*x)-1617*ln(2+3*x)+1617*ln(3+5*x)

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Maxima [A]  time = 1.34726, size = 62, normalized size = 1.24 \[ \frac{1212830 \, x^{2} + 1495689 \, x + 459996}{150 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + 1617 \, \log \left (5 \, x + 3\right ) - 1617 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/150*(1212830*x^2 + 1495689*x + 459996)/(75*x^3 + 140*x^2 + 87*x + 18) + 1617*l
og(5*x + 3) - 1617*log(3*x + 2)

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Fricas [A]  time = 0.227255, size = 101, normalized size = 2.02 \[ \frac{1212830 \, x^{2} + 242550 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 242550 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) + 1495689 \, x + 459996}{150 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/150*(1212830*x^2 + 242550*(75*x^3 + 140*x^2 + 87*x + 18)*log(5*x + 3) - 242550
*(75*x^3 + 140*x^2 + 87*x + 18)*log(3*x + 2) + 1495689*x + 459996)/(75*x^3 + 140
*x^2 + 87*x + 18)

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Sympy [A]  time = 0.395553, size = 41, normalized size = 0.82 \[ \frac{1212830 x^{2} + 1495689 x + 459996}{11250 x^{3} + 21000 x^{2} + 13050 x + 2700} + 1617 \log{\left (x + \frac{3}{5} \right )} - 1617 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(1212830*x**2 + 1495689*x + 459996)/(11250*x**3 + 21000*x**2 + 13050*x + 2700) +
1617*log(x + 3/5) - 1617*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.21715, size = 66, normalized size = 1.32 \[ \frac{343}{3 \,{\left (3 \, x + 2\right )}} - \frac{1089 \,{\left (\frac{14}{3 \, x + 2} - 59\right )}}{2 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + 1617 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/3/(3*x + 2) - 1089/2*(14/(3*x + 2) - 59)/(1/(3*x + 2) - 5)^2 + 1617*ln(abs(-
1/(3*x + 2) + 5))