3.1606 \(\int \frac{(2+3 x)^2}{(1-2 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=54 \[ \frac{49}{1331 (1-2 x)}-\frac{14}{1331 (5 x+3)}-\frac{1}{1210 (5 x+3)^2}-\frac{273 \log (1-2 x)}{14641}+\frac{273 \log (5 x+3)}{14641} \]

[Out]

49/(1331*(1 - 2*x)) - 1/(1210*(3 + 5*x)^2) - 14/(1331*(3 + 5*x)) - (273*Log[1 -
2*x])/14641 + (273*Log[3 + 5*x])/14641

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Rubi [A]  time = 0.0608409, antiderivative size = 54, 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 \[ \frac{49}{1331 (1-2 x)}-\frac{14}{1331 (5 x+3)}-\frac{1}{1210 (5 x+3)^2}-\frac{273 \log (1-2 x)}{14641}+\frac{273 \log (5 x+3)}{14641} \]

Antiderivative was successfully verified.

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

[Out]

49/(1331*(1 - 2*x)) - 1/(1210*(3 + 5*x)^2) - 14/(1331*(3 + 5*x)) - (273*Log[1 -
2*x])/14641 + (273*Log[3 + 5*x])/14641

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Rubi in Sympy [A]  time = 8.89647, size = 42, normalized size = 0.78 \[ - \frac{273 \log{\left (- 2 x + 1 \right )}}{14641} + \frac{273 \log{\left (5 x + 3 \right )}}{14641} - \frac{14}{1331 \left (5 x + 3\right )} - \frac{1}{1210 \left (5 x + 3\right )^{2}} + \frac{49}{1331 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-273*log(-2*x + 1)/14641 + 273*log(5*x + 3)/14641 - 14/(1331*(5*x + 3)) - 1/(121
0*(5*x + 3)**2) + 49/(1331*(-2*x + 1))

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Mathematica [A]  time = 0.0452094, size = 47, normalized size = 0.87 \[ \frac{-\frac{11 \left (13650 x^2+14862 x+3979\right )}{(2 x-1) (5 x+3)^2}-2730 \log (1-2 x)+2730 \log (10 x+6)}{146410} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(3979 + 14862*x + 13650*x^2))/((-1 + 2*x)*(3 + 5*x)^2) - 2730*Log[1 - 2*x]
+ 2730*Log[6 + 10*x])/146410

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Maple [A]  time = 0.016, size = 45, normalized size = 0.8 \[ -{\frac{1}{1210\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{14}{3993+6655\,x}}+{\frac{273\,\ln \left ( 3+5\,x \right ) }{14641}}-{\frac{49}{-1331+2662\,x}}-{\frac{273\,\ln \left ( -1+2\,x \right ) }{14641}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/1210/(3+5*x)^2-14/1331/(3+5*x)+273/14641*ln(3+5*x)-49/1331/(-1+2*x)-273/14641
*ln(-1+2*x)

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Maxima [A]  time = 1.34971, size = 62, normalized size = 1.15 \[ -\frac{13650 \, x^{2} + 14862 \, x + 3979}{13310 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{273}{14641} \, \log \left (5 \, x + 3\right ) - \frac{273}{14641} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/13310*(13650*x^2 + 14862*x + 3979)/(50*x^3 + 35*x^2 - 12*x - 9) + 273/14641*l
og(5*x + 3) - 273/14641*log(2*x - 1)

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Fricas [A]  time = 0.205644, size = 101, normalized size = 1.87 \[ -\frac{150150 \, x^{2} - 2730 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 2730 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 163482 \, x + 43769}{146410 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/146410*(150150*x^2 - 2730*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) + 2730*(5
0*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) + 163482*x + 43769)/(50*x^3 + 35*x^2 - 1
2*x - 9)

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Sympy [A]  time = 0.401378, size = 44, normalized size = 0.81 \[ - \frac{13650 x^{2} + 14862 x + 3979}{665500 x^{3} + 465850 x^{2} - 159720 x - 119790} - \frac{273 \log{\left (x - \frac{1}{2} \right )}}{14641} + \frac{273 \log{\left (x + \frac{3}{5} \right )}}{14641} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(13650*x**2 + 14862*x + 3979)/(665500*x**3 + 465850*x**2 - 159720*x - 119790) -
273*log(x - 1/2)/14641 + 273*log(x + 3/5)/14641

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GIAC/XCAS [A]  time = 0.206149, size = 69, normalized size = 1.28 \[ -\frac{49}{1331 \,{\left (2 \, x - 1\right )}} + \frac{2 \,{\left (\frac{792}{2 \, x - 1} + 355\right )}}{14641 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} + \frac{273}{14641} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-49/1331/(2*x - 1) + 2/14641*(792/(2*x - 1) + 355)/(11/(2*x - 1) + 5)^2 + 273/14
641*ln(abs(-11/(2*x - 1) - 5))