3.1421 \(\int \frac{(2+3 x)^4 (3+5 x)}{1-2 x} \, dx\)

Optimal. Leaf size=44 \[ -\frac{81 x^5}{2}-\frac{3051 x^4}{16}-\frac{3321 x^3}{8}-\frac{18987 x^2}{32}-\frac{24875 x}{32}-\frac{26411}{64} \log (1-2 x) \]

[Out]

(-24875*x)/32 - (18987*x^2)/32 - (3321*x^3)/8 - (3051*x^4)/16 - (81*x^5)/2 - (26
411*Log[1 - 2*x])/64

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Rubi [A]  time = 0.042241, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{81 x^5}{2}-\frac{3051 x^4}{16}-\frac{3321 x^3}{8}-\frac{18987 x^2}{32}-\frac{24875 x}{32}-\frac{26411}{64} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-24875*x)/32 - (18987*x^2)/32 - (3321*x^3)/8 - (3051*x^4)/16 - (81*x^5)/2 - (26
411*Log[1 - 2*x])/64

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{81 x^{5}}{2} - \frac{3051 x^{4}}{16} - \frac{3321 x^{3}}{8} - \frac{26411 \log{\left (- 2 x + 1 \right )}}{64} + \int \left (- \frac{24875}{32}\right )\, dx - \frac{18987 \int x\, dx}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81*x**5/2 - 3051*x**4/16 - 3321*x**3/8 - 26411*log(-2*x + 1)/64 + Integral(-248
75/32, x) - 18987*Integral(x, x)/16

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Mathematica [A]  time = 0.0215886, size = 37, normalized size = 0.84 \[ \frac{1}{256} \left (-10368 x^5-48816 x^4-106272 x^3-151896 x^2-199000 x-105644 \log (1-2 x)+154133\right ) \]

Antiderivative was successfully verified.

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

[Out]

(154133 - 199000*x - 151896*x^2 - 106272*x^3 - 48816*x^4 - 10368*x^5 - 105644*Lo
g[1 - 2*x])/256

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Maple [A]  time = 0.003, size = 33, normalized size = 0.8 \[ -{\frac{81\,{x}^{5}}{2}}-{\frac{3051\,{x}^{4}}{16}}-{\frac{3321\,{x}^{3}}{8}}-{\frac{18987\,{x}^{2}}{32}}-{\frac{24875\,x}{32}}-{\frac{26411\,\ln \left ( -1+2\,x \right ) }{64}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81/2*x^5-3051/16*x^4-3321/8*x^3-18987/32*x^2-24875/32*x-26411/64*ln(-1+2*x)

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Maxima [A]  time = 1.34839, size = 43, normalized size = 0.98 \[ -\frac{81}{2} \, x^{5} - \frac{3051}{16} \, x^{4} - \frac{3321}{8} \, x^{3} - \frac{18987}{32} \, x^{2} - \frac{24875}{32} \, x - \frac{26411}{64} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81/2*x^5 - 3051/16*x^4 - 3321/8*x^3 - 18987/32*x^2 - 24875/32*x - 26411/64*log(
2*x - 1)

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Fricas [A]  time = 0.208693, size = 43, normalized size = 0.98 \[ -\frac{81}{2} \, x^{5} - \frac{3051}{16} \, x^{4} - \frac{3321}{8} \, x^{3} - \frac{18987}{32} \, x^{2} - \frac{24875}{32} \, x - \frac{26411}{64} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81/2*x^5 - 3051/16*x^4 - 3321/8*x^3 - 18987/32*x^2 - 24875/32*x - 26411/64*log(
2*x - 1)

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Sympy [A]  time = 0.182054, size = 42, normalized size = 0.95 \[ - \frac{81 x^{5}}{2} - \frac{3051 x^{4}}{16} - \frac{3321 x^{3}}{8} - \frac{18987 x^{2}}{32} - \frac{24875 x}{32} - \frac{26411 \log{\left (2 x - 1 \right )}}{64} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81*x**5/2 - 3051*x**4/16 - 3321*x**3/8 - 18987*x**2/32 - 24875*x/32 - 26411*log
(2*x - 1)/64

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GIAC/XCAS [A]  time = 0.208205, size = 45, normalized size = 1.02 \[ -\frac{81}{2} \, x^{5} - \frac{3051}{16} \, x^{4} - \frac{3321}{8} \, x^{3} - \frac{18987}{32} \, x^{2} - \frac{24875}{32} \, x - \frac{26411}{64} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81/2*x^5 - 3051/16*x^4 - 3321/8*x^3 - 18987/32*x^2 - 24875/32*x - 26411/64*ln(a
bs(2*x - 1))