3.1214 \(\int \frac{1-2 x}{(2+3 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=46 \[ \frac{21}{3 x+2}+\frac{68}{5 x+3}-\frac{11}{2 (5 x+3)^2}-309 \log (3 x+2)+309 \log (5 x+3) \]

[Out]

21/(2 + 3*x) - 11/(2*(3 + 5*x)^2) + 68/(3 + 5*x) - 309*Log[2 + 3*x] + 309*Log[3
+ 5*x]

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Rubi [A]  time = 0.0546662, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{21}{3 x+2}+\frac{68}{5 x+3}-\frac{11}{2 (5 x+3)^2}-309 \log (3 x+2)+309 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

21/(2 + 3*x) - 11/(2*(3 + 5*x)^2) + 68/(3 + 5*x) - 309*Log[2 + 3*x] + 309*Log[3
+ 5*x]

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Rubi in Sympy [A]  time = 7.93288, size = 39, normalized size = 0.85 \[ - 309 \log{\left (3 x + 2 \right )} + 309 \log{\left (5 x + 3 \right )} + \frac{68}{5 x + 3} - \frac{11}{2 \left (5 x + 3\right )^{2}} + \frac{21}{3 x + 2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-309*log(3*x + 2) + 309*log(5*x + 3) + 68/(5*x + 3) - 11/(2*(5*x + 3)**2) + 21/(
3*x + 2)

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Mathematica [A]  time = 0.0298167, size = 48, normalized size = 1.04 \[ \frac{21}{3 x+2}+\frac{68}{5 x+3}-\frac{11}{2 (5 x+3)^2}-309 \log (3 x+2)+309 \log (-3 (5 x+3)) \]

Antiderivative was successfully verified.

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

[Out]

21/(2 + 3*x) - 11/(2*(3 + 5*x)^2) + 68/(3 + 5*x) - 309*Log[2 + 3*x] + 309*Log[-3
*(3 + 5*x)]

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Maple [A]  time = 0.014, size = 45, normalized size = 1. \[ 21\, \left ( 2+3\,x \right ) ^{-1}-{\frac{11}{2\, \left ( 3+5\,x \right ) ^{2}}}+68\, \left ( 3+5\,x \right ) ^{-1}-309\,\ln \left ( 2+3\,x \right ) +309\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

21/(2+3*x)-11/2/(3+5*x)^2+68/(3+5*x)-309*ln(2+3*x)+309*ln(3+5*x)

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Maxima [A]  time = 1.32709, size = 62, normalized size = 1.35 \[ \frac{3090 \, x^{2} + 3811 \, x + 1172}{2 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + 309 \, \log \left (5 \, x + 3\right ) - 309 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(3090*x^2 + 3811*x + 1172)/(75*x^3 + 140*x^2 + 87*x + 18) + 309*log(5*x + 3)
- 309*log(3*x + 2)

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Fricas [A]  time = 0.210728, size = 101, normalized size = 2.2 \[ \frac{3090 \, x^{2} + 618 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 618 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) + 3811 \, x + 1172}{2 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(3090*x^2 + 618*(75*x^3 + 140*x^2 + 87*x + 18)*log(5*x + 3) - 618*(75*x^3 +
140*x^2 + 87*x + 18)*log(3*x + 2) + 3811*x + 1172)/(75*x^3 + 140*x^2 + 87*x + 18
)

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Sympy [A]  time = 0.356907, size = 41, normalized size = 0.89 \[ \frac{3090 x^{2} + 3811 x + 1172}{150 x^{3} + 280 x^{2} + 174 x + 36} + 309 \log{\left (x + \frac{3}{5} \right )} - 309 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(3090*x**2 + 3811*x + 1172)/(150*x**3 + 280*x**2 + 174*x + 36) + 309*log(x + 3/5
) - 309*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.209807, size = 66, normalized size = 1.43 \[ \frac{21}{3 \, x + 2} - \frac{15 \,{\left (\frac{202}{3 \, x + 2} - 845\right )}}{2 \,{\left (\frac{1}{3 \, x + 2} - 5\right )}^{2}} + 309 \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

21/(3*x + 2) - 15/2*(202/(3*x + 2) - 845)/(1/(3*x + 2) - 5)^2 + 309*ln(abs(-1/(3
*x + 2) + 5))