3.1589 \(\int \frac{(2+3 x)^5}{(1-2 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=55 \[ \frac{243 x^2}{200}+\frac{3807 x}{500}+\frac{16807}{1936 (1-2 x)}-\frac{1}{75625 (5 x+3)}+\frac{228095 \log (1-2 x)}{21296}+\frac{169 \log (5 x+3)}{831875} \]

[Out]

16807/(1936*(1 - 2*x)) + (3807*x)/500 + (243*x^2)/200 - 1/(75625*(3 + 5*x)) + (2
28095*Log[1 - 2*x])/21296 + (169*Log[3 + 5*x])/831875

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Rubi [A]  time = 0.0659693, antiderivative size = 55, 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 \[ \frac{243 x^2}{200}+\frac{3807 x}{500}+\frac{16807}{1936 (1-2 x)}-\frac{1}{75625 (5 x+3)}+\frac{228095 \log (1-2 x)}{21296}+\frac{169 \log (5 x+3)}{831875} \]

Antiderivative was successfully verified.

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

[Out]

16807/(1936*(1 - 2*x)) + (3807*x)/500 + (243*x^2)/200 - 1/(75625*(3 + 5*x)) + (2
28095*Log[1 - 2*x])/21296 + (169*Log[3 + 5*x])/831875

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{228095 \log{\left (- 2 x + 1 \right )}}{21296} + \frac{169 \log{\left (5 x + 3 \right )}}{831875} + \int \frac{3807}{500}\, dx + \frac{243 \int x\, dx}{100} - \frac{1}{75625 \left (5 x + 3\right )} + \frac{16807}{1936 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

228095*log(-2*x + 1)/21296 + 169*log(5*x + 3)/831875 + Integral(3807/500, x) + 2
43*Integral(x, x)/100 - 1/(75625*(5*x + 3)) + 16807/(1936*(-2*x + 1))

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Mathematica [A]  time = 0.0500594, size = 56, normalized size = 1.02 \[ \frac{-\frac{11 (52521907 x+31513109)}{10 x^2+x-3}+1796850 (3 x+2)^2+26593380 (3 x+2)[phone] \log (3-6 x)+2704 \log (-3 (5 x+3))}{13310000} \]

Antiderivative was successfully verified.

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

[Out]

(26593380*(2 + 3*x) + 1796850*(2 + 3*x)^2 - (11*(31513109 + 52521907*x))/(-3 + x
+ 10*x^2) + 142559375*Log[3 - 6*x] + 2704*Log[-3*(3 + 5*x)])/13310000

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Maple [A]  time = 0.015, size = 44, normalized size = 0.8 \[{\frac{243\,{x}^{2}}{200}}+{\frac{3807\,x}{500}}-{\frac{1}{226875+378125\,x}}+{\frac{169\,\ln \left ( 3+5\,x \right ) }{831875}}-{\frac{16807}{-1936+3872\,x}}+{\frac{228095\,\ln \left ( -1+2\,x \right ) }{21296}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

243/200*x^2+3807/500*x-1/75625/(3+5*x)+169/831875*ln(3+5*x)-16807/1936/(-1+2*x)+
228095/21296*ln(-1+2*x)

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Maxima [A]  time = 1.37529, size = 57, normalized size = 1.04 \[ \frac{243}{200} \, x^{2} + \frac{3807}{500} \, x - \frac{52521907 \, x + 31513109}{1210000 \,{\left (10 \, x^{2} + x - 3\right )}} + \frac{169}{831875} \, \log \left (5 \, x + 3\right ) + \frac{228095}{21296} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

243/200*x^2 + 3807/500*x - 1/1210000*(52521907*x + 31513109)/(10*x^2 + x - 3) +
169/831875*log(5*x + 3) + 228095/21296*log(2*x - 1)

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Fricas [A]  time = 0.214042, size = 86, normalized size = 1.56 \[ \frac{161716500 \, x^{4} + 1029595050 \, x^{3} + 52827390 \, x^{2} + 2704 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 142559375 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 881767997 \, x - 346644199}{13310000 \,{\left (10 \, x^{2} + x - 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/13310000*(161716500*x^4 + 1029595050*x^3 + 52827390*x^2 + 2704*(10*x^2 + x - 3
)*log(5*x + 3) + 142559375*(10*x^2 + x - 3)*log(2*x - 1) - 881767997*x - 3466441
99)/(10*x^2 + x - 3)

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Sympy [A]  time = 0.398456, size = 46, normalized size = 0.84 \[ \frac{243 x^{2}}{200} + \frac{3807 x}{500} - \frac{52521907 x + 31513109}{12100000 x^{2} + 1210000 x - 3630000} + \frac{228095 \log{\left (x - \frac{1}{2} \right )}}{21296} + \frac{169 \log{\left (x + \frac{3}{5} \right )}}{831875} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

243*x**2/200 + 3807*x/500 - (52521907*x + 31513109)/(12100000*x**2 + 1210000*x -
3630000) + 228095*log(x - 1/2)/21296 + 169*log(x + 3/5)/831875

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GIAC/XCAS [A]  time = 0.210546, size = 115, normalized size = 2.09 \[ -\frac{{\left (5 \, x + 3\right )}^{2}{\left (\frac{12829509}{5 \, x + 3} - \frac{142651871}{{\left (5 \, x + 3\right )}^{2}} + 646866\right )}}{6655000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} - \frac{1}{75625 \,{\left (5 \, x + 3\right )}} - \frac{107109}{10000} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{228095}{21296} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6655000*(5*x + 3)^2*(12829509/(5*x + 3) - 142651871/(5*x + 3)^2 + 646866)/(11
/(5*x + 3) - 2) - 1/75625/(5*x + 3) - 107109/10000*ln(1/5*abs(5*x + 3)/(5*x + 3)
^2) + 228095/21296*ln(abs(-11/(5*x + 3) + 2))