3.1471 \(\int \frac{(2+3 x)^5}{(1-2 x) (3+5 x)} \, dx\)

Optimal. Leaf size=47 \[ -\frac{243 x^4}{40}-\frac{2619 x^3}{100}-\frac{107433 x^2}{2000}-\frac{848277 x}{10000}-\frac{16807}{352} \log (1-2 x)+\frac{\log (5 x+3)}{34375} \]

[Out]

(-848277*x)/10000 - (107433*x^2)/2000 - (2619*x^3)/100 - (243*x^4)/40 - (16807*L
og[1 - 2*x])/352 + Log[3 + 5*x]/34375

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Rubi [A]  time = 0.0508987, antiderivative size = 47, 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 \[ -\frac{243 x^4}{40}-\frac{2619 x^3}{100}-\frac{107433 x^2}{2000}-\frac{848277 x}{10000}-\frac{16807}{352} \log (1-2 x)+\frac{\log (5 x+3)}{34375} \]

Antiderivative was successfully verified.

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

[Out]

(-848277*x)/10000 - (107433*x^2)/2000 - (2619*x^3)/100 - (243*x^4)/40 - (16807*L
og[1 - 2*x])/352 + Log[3 + 5*x]/34375

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{243 x^{4}}{40} - \frac{2619 x^{3}}{100} - \frac{16807 \log{\left (- 2 x + 1 \right )}}{352} + \frac{\log{\left (5 x + 3 \right )}}{34375} + \int \left (- \frac{848277}{10000}\right )\, dx - \frac{107433 \int x\, dx}{1000} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x**4/40 - 2619*x**3/100 - 16807*log(-2*x + 1)/352 + log(5*x + 3)/34375 + In
tegral(-848277/10000, x) - 107433*Integral(x, x)/1000

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Mathematica [A]  time = 0.025886, size = 45, normalized size = 0.96 \[ \frac{-110 \left (60750 x^4+261900 x^3+537165 x^2+848277 x+392378\right )-52521875 \log (3-6 x)+32 \log (-3 (5 x+3))}{1100000} \]

Antiderivative was successfully verified.

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

[Out]

(-110*(392378 + 848277*x + 537165*x^2 + 261900*x^3 + 60750*x^4) - 52521875*Log[3
- 6*x] + 32*Log[-3*(3 + 5*x)])/1100000

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Maple [A]  time = 0.008, size = 36, normalized size = 0.8 \[ -{\frac{243\,{x}^{4}}{40}}-{\frac{2619\,{x}^{3}}{100}}-{\frac{107433\,{x}^{2}}{2000}}-{\frac{848277\,x}{10000}}+{\frac{\ln \left ( 3+5\,x \right ) }{34375}}-{\frac{16807\,\ln \left ( -1+2\,x \right ) }{352}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/40*x^4-2619/100*x^3-107433/2000*x^2-848277/10000*x+1/34375*ln(3+5*x)-16807/
352*ln(-1+2*x)

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Maxima [A]  time = 1.34975, size = 47, normalized size = 1. \[ -\frac{243}{40} \, x^{4} - \frac{2619}{100} \, x^{3} - \frac{107433}{2000} \, x^{2} - \frac{848277}{10000} \, x + \frac{1}{34375} \, \log \left (5 \, x + 3\right ) - \frac{16807}{352} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/40*x^4 - 2619/100*x^3 - 107433/2000*x^2 - 848277/10000*x + 1/34375*log(5*x
+ 3) - 16807/352*log(2*x - 1)

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Fricas [A]  time = 0.229274, size = 47, normalized size = 1. \[ -\frac{243}{40} \, x^{4} - \frac{2619}{100} \, x^{3} - \frac{107433}{2000} \, x^{2} - \frac{848277}{10000} \, x + \frac{1}{34375} \, \log \left (5 \, x + 3\right ) - \frac{16807}{352} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/40*x^4 - 2619/100*x^3 - 107433/2000*x^2 - 848277/10000*x + 1/34375*log(5*x
+ 3) - 16807/352*log(2*x - 1)

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Sympy [A]  time = 0.299308, size = 42, normalized size = 0.89 \[ - \frac{243 x^{4}}{40} - \frac{2619 x^{3}}{100} - \frac{107433 x^{2}}{2000} - \frac{848277 x}{10000} - \frac{16807 \log{\left (x - \frac{1}{2} \right )}}{352} + \frac{\log{\left (x + \frac{3}{5} \right )}}{34375} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x**4/40 - 2619*x**3/100 - 107433*x**2/2000 - 848277*x/10000 - 16807*log(x -
1/2)/352 + log(x + 3/5)/34375

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GIAC/XCAS [A]  time = 0.216671, size = 50, normalized size = 1.06 \[ -\frac{243}{40} \, x^{4} - \frac{2619}{100} \, x^{3} - \frac{107433}{2000} \, x^{2} - \frac{848277}{10000} \, x + \frac{1}{34375} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{16807}{352} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/40*x^4 - 2619/100*x^3 - 107433/2000*x^2 - 848277/10000*x + 1/34375*ln(abs(5
*x + 3)) - 16807/352*ln(abs(2*x - 1))