3.1472 \(\int \frac{(2+3 x)^4}{(1-2 x) (3+5 x)} \, dx\)

Optimal. Leaf size=40 \[ -\frac{27 x^3}{10}-\frac{2079 x^2}{200}-\frac{21951 x}{1000}-\frac{2401}{176} \log (1-2 x)+\frac{\log (5 x+3)}{6875} \]

[Out]

(-21951*x)/1000 - (2079*x^2)/200 - (27*x^3)/10 - (2401*Log[1 - 2*x])/176 + Log[3
+ 5*x]/6875

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Rubi [A]  time = 0.048319, antiderivative size = 40, 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 \[ -\frac{27 x^3}{10}-\frac{2079 x^2}{200}-\frac{21951 x}{1000}-\frac{2401}{176} \log (1-2 x)+\frac{\log (5 x+3)}{6875} \]

Antiderivative was successfully verified.

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

[Out]

(-21951*x)/1000 - (2079*x^2)/200 - (27*x^3)/10 - (2401*Log[1 - 2*x])/176 + Log[3
+ 5*x]/6875

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{27 x^{3}}{10} - \frac{2401 \log{\left (- 2 x + 1 \right )}}{176} + \frac{\log{\left (5 x + 3 \right )}}{6875} + \int \left (- \frac{21951}{1000}\right )\, dx - \frac{2079 \int x\, dx}{100} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27*x**3/10 - 2401*log(-2*x + 1)/176 + log(5*x + 3)/6875 + Integral(-21951/1000,
x) - 2079*Integral(x, x)/100

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Mathematica [A]  time = 0.0336107, size = 43, normalized size = 1.08 \[ \frac{8 \log (-3 (5 x+3))-55 \left (2700 x^3+10395 x^2+21951 x+10814\right )}{55000}-\frac{2401}{176} \log (3-6 x) \]

Antiderivative was successfully verified.

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

[Out]

(-2401*Log[3 - 6*x])/176 + (-55*(10814 + 21951*x + 10395*x^2 + 2700*x^3) + 8*Log
[-3*(3 + 5*x)])/55000

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Maple [A]  time = 0.008, size = 31, normalized size = 0.8 \[ -{\frac{27\,{x}^{3}}{10}}-{\frac{2079\,{x}^{2}}{200}}-{\frac{21951\,x}{1000}}+{\frac{\ln \left ( 3+5\,x \right ) }{6875}}-{\frac{2401\,\ln \left ( -1+2\,x \right ) }{176}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/10*x^3-2079/200*x^2-21951/1000*x+1/6875*ln(3+5*x)-2401/176*ln(-1+2*x)

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Maxima [A]  time = 1.34284, size = 41, normalized size = 1.02 \[ -\frac{27}{10} \, x^{3} - \frac{2079}{200} \, x^{2} - \frac{21951}{1000} \, x + \frac{1}{6875} \, \log \left (5 \, x + 3\right ) - \frac{2401}{176} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/10*x^3 - 2079/200*x^2 - 21951/1000*x + 1/6875*log(5*x + 3) - 2401/176*log(2*
x - 1)

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Fricas [A]  time = 0.207644, size = 41, normalized size = 1.02 \[ -\frac{27}{10} \, x^{3} - \frac{2079}{200} \, x^{2} - \frac{21951}{1000} \, x + \frac{1}{6875} \, \log \left (5 \, x + 3\right ) - \frac{2401}{176} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/10*x^3 - 2079/200*x^2 - 21951/1000*x + 1/6875*log(5*x + 3) - 2401/176*log(2*
x - 1)

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Sympy [A]  time = 0.32157, size = 36, normalized size = 0.9 \[ - \frac{27 x^{3}}{10} - \frac{2079 x^{2}}{200} - \frac{21951 x}{1000} - \frac{2401 \log{\left (x - \frac{1}{2} \right )}}{176} + \frac{\log{\left (x + \frac{3}{5} \right )}}{6875} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27*x**3/10 - 2079*x**2/200 - 21951*x/1000 - 2401*log(x - 1/2)/176 + log(x + 3/5
)/6875

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GIAC/XCAS [A]  time = 0.20681, size = 43, normalized size = 1.08 \[ -\frac{27}{10} \, x^{3} - \frac{2079}{200} \, x^{2} - \frac{21951}{1000} \, x + \frac{1}{6875} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{2401}{176} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-27/10*x^3 - 2079/200*x^2 - 21951/1000*x + 1/6875*ln(abs(5*x + 3)) - 2401/176*ln
(abs(2*x - 1))