3.1458 \(\int \frac{(3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=30 \[ -\frac{125 x^3}{6}-\frac{575 x^2}{8}-\frac{1115 x}{8}-\frac{1331}{16} \log (1-2 x) \]

[Out]

(-1115*x)/8 - (575*x^2)/8 - (125*x^3)/6 - (1331*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0277851, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{125 x^3}{6}-\frac{575 x^2}{8}-\frac{1115 x}{8}-\frac{1331}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^3/(1 - 2*x),x]

[Out]

(-1115*x)/8 - (575*x^2)/8 - (125*x^3)/6 - (1331*Log[1 - 2*x])/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{125 x^{3}}{6} - \frac{1331 \log{\left (- 2 x + 1 \right )}}{16} + \int \left (- \frac{1115}{8}\right )\, dx - \frac{575 \int x\, dx}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*x**3/6 - 1331*log(-2*x + 1)/16 + Integral(-1115/8, x) - 575*Integral(x, x)/
4

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Mathematica [A]  time = 0.0117379, size = 30, normalized size = 1. \[ \frac{1}{96} \left (-5 \left (400 x^3+1380 x^2+2676 x-1733\right )-7986 \log (1-2 x)\right ) \]

Antiderivative was successfully verified.

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

[Out]

(-5*(-1733 + 2676*x + 1380*x^2 + 400*x^3) - 7986*Log[1 - 2*x])/96

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Maple [A]  time = 0.003, size = 23, normalized size = 0.8 \[ -{\frac{125\,{x}^{3}}{6}}-{\frac{575\,{x}^{2}}{8}}-{\frac{1115\,x}{8}}-{\frac{1331\,\ln \left ( -1+2\,x \right ) }{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^3/(1-2*x),x)

[Out]

-125/6*x^3-575/8*x^2-1115/8*x-1331/16*ln(-1+2*x)

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Maxima [A]  time = 1.33837, size = 30, normalized size = 1. \[ -\frac{125}{6} \, x^{3} - \frac{575}{8} \, x^{2} - \frac{1115}{8} \, x - \frac{1331}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/6*x^3 - 575/8*x^2 - 1115/8*x - 1331/16*log(2*x - 1)

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Fricas [A]  time = 0.211171, size = 30, normalized size = 1. \[ -\frac{125}{6} \, x^{3} - \frac{575}{8} \, x^{2} - \frac{1115}{8} \, x - \frac{1331}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/6*x^3 - 575/8*x^2 - 1115/8*x - 1331/16*log(2*x - 1)

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Sympy [A]  time = 0.151274, size = 29, normalized size = 0.97 \[ - \frac{125 x^{3}}{6} - \frac{575 x^{2}}{8} - \frac{1115 x}{8} - \frac{1331 \log{\left (2 x - 1 \right )}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3+5*x)**3/(1-2*x),x)

[Out]

-125*x**3/6 - 575*x**2/8 - 1115*x/8 - 1331*log(2*x - 1)/16

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GIAC/XCAS [A]  time = 0.21021, size = 31, normalized size = 1.03 \[ -\frac{125}{6} \, x^{3} - \frac{575}{8} \, x^{2} - \frac{1115}{8} \, x - \frac{1331}{16} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/6*x^3 - 575/8*x^2 - 1115/8*x - 1331/16*ln(abs(2*x - 1))