3.1671 \(\int \frac{(2+3 x)^4}{(1-2 x)^3 (3+5 x)^2} \, dx\)

Optimal. Leaf size=54 \[ -\frac{10633}{5324 (1-2 x)}-\frac{1}{33275 (5 x+3)}+\frac{2401}{1936 (1-2 x)^2}-\frac{47481 \log (1-2 x)}{117128}+\frac{138 \log (5 x+3)}{366025} \]

[Out]

2401/(1936*(1 - 2*x)^2) - 10633/(5324*(1 - 2*x)) - 1/(33275*(3 + 5*x)) - (47481*
Log[1 - 2*x])/117128 + (138*Log[3 + 5*x])/366025

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Rubi [A]  time = 0.0628667, 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 \[ -\frac{10633}{5324 (1-2 x)}-\frac{1}{33275 (5 x+3)}+\frac{2401}{1936 (1-2 x)^2}-\frac{47481 \log (1-2 x)}{117128}+\frac{138 \log (5 x+3)}{366025} \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)^2),x]

[Out]

2401/(1936*(1 - 2*x)^2) - 10633/(5324*(1 - 2*x)) - 1/(33275*(3 + 5*x)) - (47481*
Log[1 - 2*x])/117128 + (138*Log[3 + 5*x])/366025

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Rubi in Sympy [A]  time = 8.98642, size = 42, normalized size = 0.78 \[ - \frac{47481 \log{\left (- 2 x + 1 \right )}}{117128} + \frac{138 \log{\left (5 x + 3 \right )}}{366025} - \frac{1}{33275 \left (5 x + 3\right )} - \frac{10633}{5324 \left (- 2 x + 1\right )} + \frac{2401}{1936 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**4/(1-2*x)**3/(3+5*x)**2,x)

[Out]

-47481*log(-2*x + 1)/117128 + 138*log(5*x + 3)/366025 - 1/(33275*(5*x + 3)) - 10
633/(5324*(-2*x + 1)) + 2401/(1936*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0505429, size = 48, normalized size = 0.89 \[ \frac{\frac{11696300}{2 x-1}-\frac{176}{5 x+3}+\frac{7263025}{(1-2 x)^2}-2374050 \log (1-2 x)+2208 \log (10 x+6)}{5856400} \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^4/((1 - 2*x)^3*(3 + 5*x)^2),x]

[Out]

(7263025/(1 - 2*x)^2 + 11696300/(-1 + 2*x) - 176/(3 + 5*x) - 2374050*Log[1 - 2*x
] + 2208*Log[6 + 10*x])/5856400

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Maple [A]  time = 0.013, size = 45, normalized size = 0.8 \[ -{\frac{1}{99825+166375\,x}}+{\frac{138\,\ln \left ( 3+5\,x \right ) }{366025}}+{\frac{2401}{1936\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{10633}{-5324+10648\,x}}-{\frac{47481\,\ln \left ( -1+2\,x \right ) }{117128}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^4/(1-2*x)^3/(3+5*x)^2,x)

[Out]

-1/33275/(3+5*x)+138/366025*ln(3+5*x)+2401/1936/(-1+2*x)^2+10633/5324/(-1+2*x)-4
7481/117128*ln(-1+2*x)

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Maxima [A]  time = 1.3423, size = 62, normalized size = 1.15 \[ \frac{10632936 \, x^{2} + 4364739 \, x - 1209091}{532400 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{138}{366025} \, \log \left (5 \, x + 3\right ) - \frac{47481}{117128} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="maxima")

[Out]

1/532400*(10632936*x^2 + 4364739*x - 1209091)/(20*x^3 - 8*x^2 - 7*x + 3) + 138/3
66025*log(5*x + 3) - 47481/117128*log(2*x - 1)

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Fricas [A]  time = 0.208127, size = 101, normalized size = 1.87 \[ \frac{116962296 \, x^{2} + 2208 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 2374050 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 48012129 \, x - 13300001}{5856400 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="fricas")

[Out]

1/5856400*(116962296*x^2 + 2208*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) - 237405
0*(20*x^3 - 8*x^2 - 7*x + 3)*log(2*x - 1) + 48012129*x - 13300001)/(20*x^3 - 8*x
^2 - 7*x + 3)

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Sympy [A]  time = 0.489822, size = 44, normalized size = 0.81 \[ \frac{10632936 x^{2} + 4364739 x - 1209091}{10648000 x^{3} - 4259200 x^{2} - 3726800 x + 1597200} - \frac{47481 \log{\left (x - \frac{1}{2} \right )}}{117128} + \frac{138 \log{\left (x + \frac{3}{5} \right )}}{366025} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**4/(1-2*x)**3/(3+5*x)**2,x)

[Out]

(10632936*x**2 + 4364739*x - 1209091)/(10648000*x**3 - 4259200*x**2 - 3726800*x
+ 1597200) - 47481*log(x - 1/2)/117128 + 138*log(x + 3/5)/366025

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GIAC/XCAS [A]  time = 0.214788, size = 93, normalized size = 1.72 \[ -\frac{1}{33275 \,{\left (5 \, x + 3\right )}} - \frac{1715 \,{\left (\frac{297}{5 \, x + 3} - 89\right )}}{58564 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} + \frac{81}{200} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{47481}{117128} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="giac")

[Out]

-1/33275/(5*x + 3) - 1715/58564*(297/(5*x + 3) - 89)/(11/(5*x + 3) - 2)^2 + 81/2
00*ln(1/5*abs(5*x + 3)/(5*x + 3)^2) - 47481/117128*ln(abs(-11/(5*x + 3) + 2))