3.1447 \(\int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^5} \, dx\)

Optimal. Leaf size=65 \[ -\frac{242}{2401 (3 x+2)}-\frac{121}{686 (3 x+2)^2}+\frac{68}{1323 (3 x+2)^3}-\frac{1}{252 (3 x+2)^4}-\frac{484 \log (1-2 x)}{16807}+\frac{484 \log (3 x+2)}{16807} \]

[Out]

-1/(252*(2 + 3*x)^4) + 68/(1323*(2 + 3*x)^3) - 121/(686*(2 + 3*x)^2) - 242/(2401
*(2 + 3*x)) - (484*Log[1 - 2*x])/16807 + (484*Log[2 + 3*x])/16807

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Rubi [A]  time = 0.0664307, antiderivative size = 65, 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 \[ -\frac{242}{2401 (3 x+2)}-\frac{121}{686 (3 x+2)^2}+\frac{68}{1323 (3 x+2)^3}-\frac{1}{252 (3 x+2)^4}-\frac{484 \log (1-2 x)}{16807}+\frac{484 \log (3 x+2)}{16807} \]

Antiderivative was successfully verified.

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

[Out]

-1/(252*(2 + 3*x)^4) + 68/(1323*(2 + 3*x)^3) - 121/(686*(2 + 3*x)^2) - 242/(2401
*(2 + 3*x)) - (484*Log[1 - 2*x])/16807 + (484*Log[2 + 3*x])/16807

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Rubi in Sympy [A]  time = 10.2172, size = 56, normalized size = 0.86 \[ - \frac{484 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{484 \log{\left (3 x + 2 \right )}}{16807} - \frac{242}{2401 \left (3 x + 2\right )} - \frac{121}{686 \left (3 x + 2\right )^{2}} + \frac{68}{1323 \left (3 x + 2\right )^{3}} - \frac{1}{252 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-484*log(-2*x + 1)/16807 + 484*log(3*x + 2)/16807 - 242/(2401*(3*x + 2)) - 121/(
686*(3*x + 2)**2) + 68/(1323*(3*x + 2)**3) - 1/(252*(3*x + 2)**4)

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Mathematica [A]  time = 0.0487053, size = 47, normalized size = 0.72 \[ \frac{2 \left (-\frac{7 \left (705672 x^3+1822986 x^2+1449768 x+366413\right )}{8 (3 x+2)^4}-6534 \log (1-2 x)+6534 \log (6 x+4)\right )}{453789} \]

Antiderivative was successfully verified.

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

[Out]

(2*((-7*(366413 + 1449768*x + 1822986*x^2 + 705672*x^3))/(8*(2 + 3*x)^4) - 6534*
Log[1 - 2*x] + 6534*Log[4 + 6*x]))/453789

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Maple [A]  time = 0.012, size = 54, normalized size = 0.8 \[ -{\frac{1}{252\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{68}{1323\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{121}{686\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{242}{4802+7203\,x}}+{\frac{484\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{484\,\ln \left ( -1+2\,x \right ) }{16807}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/252/(2+3*x)^4+68/1323/(2+3*x)^3-121/686/(2+3*x)^2-242/2401/(2+3*x)+484/16807*
ln(2+3*x)-484/16807*ln(-1+2*x)

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Maxima [A]  time = 1.33688, size = 76, normalized size = 1.17 \[ -\frac{705672 \, x^{3} + 1822986 \, x^{2} + 1449768 \, x + 366413}{259308 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{484}{16807} \, \log \left (3 \, x + 2\right ) - \frac{484}{16807} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/259308*(705672*x^3 + 1822986*x^2 + 1449768*x + 366413)/(81*x^4 + 216*x^3 + 21
6*x^2 + 96*x + 16) + 484/16807*log(3*x + 2) - 484/16807*log(2*x - 1)

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Fricas [A]  time = 0.215767, size = 128, normalized size = 1.97 \[ -\frac{4939704 \, x^{3} + 12760902 \, x^{2} - 52272 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 52272 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (2 \, x - 1\right ) + 10148376 \, x + 2564891}{1815156 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1815156*(4939704*x^3 + 12760902*x^2 - 52272*(81*x^4 + 216*x^3 + 216*x^2 + 96*
x + 16)*log(3*x + 2) + 52272*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(2*x -
1) + 10148376*x + 2564891)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)

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Sympy [A]  time = 0.474459, size = 54, normalized size = 0.83 \[ - \frac{705672 x^{3} + 1822986 x^{2} + 1449768 x + 366413}{21003948 x^{4} + 56010528 x^{3} + 56010528 x^{2} + 24893568 x + 4148928} - \frac{484 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{484 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(705672*x**3 + 1822986*x**2 + 1449768*x + 366413)/(21003948*x**4 + 56010528*x**
3 + 56010528*x**2 + 24893568*x + 4148928) - 484*log(x - 1/2)/16807 + 484*log(x +
2/3)/16807

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GIAC/XCAS [A]  time = 0.212201, size = 70, normalized size = 1.08 \[ -\frac{242}{2401 \,{\left (3 \, x + 2\right )}} - \frac{121}{686 \,{\left (3 \, x + 2\right )}^{2}} + \frac{68}{1323 \,{\left (3 \, x + 2\right )}^{3}} - \frac{1}{252 \,{\left (3 \, x + 2\right )}^{4}} - \frac{484}{16807} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-242/2401/(3*x + 2) - 121/686/(3*x + 2)^2 + 68/1323/(3*x + 2)^3 - 1/252/(3*x + 2
)^4 - 484/16807*ln(abs(-7/(3*x + 2) + 2))