3.1575 \(\int \frac{(2+3 x)^4}{(1-2 x)^2 (3+5 x)} \, dx\)

Optimal. Leaf size=44 \[ \frac{81 x^2}{40}+\frac{621 x}{50}+\frac{2401}{176 (1-2 x)}+\frac{33271 \log (1-2 x)}{1936}+\frac{\log (5 x+3)}{15125} \]

[Out]

2401/(176*(1 - 2*x)) + (621*x)/50 + (81*x^2)/40 + (33271*Log[1 - 2*x])/1936 + Lo
g[3 + 5*x]/15125

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Rubi [A]  time = 0.0512552, antiderivative size = 44, 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 \[ \frac{81 x^2}{40}+\frac{621 x}{50}+\frac{2401}{176 (1-2 x)}+\frac{33271 \log (1-2 x)}{1936}+\frac{\log (5 x+3)}{15125} \]

Antiderivative was successfully verified.

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

[Out]

2401/(176*(1 - 2*x)) + (621*x)/50 + (81*x^2)/40 + (33271*Log[1 - 2*x])/1936 + Lo
g[3 + 5*x]/15125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{33271 \log{\left (- 2 x + 1 \right )}}{1936} + \frac{\log{\left (5 x + 3 \right )}}{15125} + \int \frac{621}{50}\, dx + \frac{81 \int x\, dx}{20} + \frac{2401}{176 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

33271*log(-2*x + 1)/1936 + log(5*x + 3)/15125 + Integral(621/50, x) + 81*Integra
l(x, x)/20 + 2401/(176*(-2*x + 1))

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Mathematica [A]  time = 0.0374559, size = 45, normalized size = 1.02 \[ \frac{81 x^2}{40}+\frac{621 x}{50}+\frac{2401}{176-352 x}+\frac{33271 \log (5-10 x)}{1936}+\frac{\log (5 x+3)}{15125}+\frac{6723}{1000} \]

Antiderivative was successfully verified.

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

[Out]

6723/1000 + 2401/(176 - 352*x) + (621*x)/50 + (81*x^2)/40 + (33271*Log[5 - 10*x]
)/1936 + Log[3 + 5*x]/15125

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Maple [A]  time = 0.011, size = 35, normalized size = 0.8 \[{\frac{81\,{x}^{2}}{40}}+{\frac{621\,x}{50}}+{\frac{\ln \left ( 3+5\,x \right ) }{15125}}-{\frac{2401}{-176+352\,x}}+{\frac{33271\,\ln \left ( -1+2\,x \right ) }{1936}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

81/40*x^2+621/50*x+1/15125*ln(3+5*x)-2401/176/(-1+2*x)+33271/1936*ln(-1+2*x)

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Maxima [A]  time = 1.34457, size = 46, normalized size = 1.05 \[ \frac{81}{40} \, x^{2} + \frac{621}{50} \, x - \frac{2401}{176 \,{\left (2 \, x - 1\right )}} + \frac{1}{15125} \, \log \left (5 \, x + 3\right ) + \frac{33271}{1936} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

81/40*x^2 + 621/50*x - 2401/176/(2*x - 1) + 1/15125*log(5*x + 3) + 33271/1936*lo
g(2*x - 1)

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Fricas [A]  time = 0.215956, size = 68, normalized size = 1.55 \[ \frac{980100 \, x^{3} + 5521230 \, x^{2} + 16 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 4158875 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 3005640 \, x - 3301375}{242000 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/242000*(980100*x^3 + 5521230*x^2 + 16*(2*x - 1)*log(5*x + 3) + 4158875*(2*x -
1)*log(2*x - 1) - 3005640*x - 3301375)/(2*x - 1)

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Sympy [A]  time = 0.323084, size = 36, normalized size = 0.82 \[ \frac{81 x^{2}}{40} + \frac{621 x}{50} + \frac{33271 \log{\left (x - \frac{1}{2} \right )}}{1936} + \frac{\log{\left (x + \frac{3}{5} \right )}}{15125} - \frac{2401}{352 x - 176} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

81*x**2/40 + 621*x/50 + 33271*log(x - 1/2)/1936 + log(x + 3/5)/15125 - 2401/(352
*x - 176)

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GIAC/XCAS [A]  time = 0.208222, size = 85, normalized size = 1.93 \[ \frac{27}{800} \,{\left (2 \, x - 1\right )}^{2}{\left (\frac{214}{2 \, x - 1} + 15\right )} - \frac{2401}{176 \,{\left (2 \, x - 1\right )}} - \frac{34371}{2000} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{15125} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

27/800*(2*x - 1)^2*(214/(2*x - 1) + 15) - 2401/176/(2*x - 1) - 34371/2000*ln(1/2
*abs(2*x - 1)/(2*x - 1)^2) + 1/15125*ln(abs(-11/(2*x - 1) - 5))