3.1632 \(\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=52 \[ -\frac{225 x^3}{8}-\frac{6345 x^2}{32}-\frac{14031 x}{16}-\frac{91091}{64 (1-2 x)}+\frac{41503}{128 (1-2 x)^2}-\frac{39977}{32} \log (1-2 x) \]

[Out]

41503/(128*(1 - 2*x)^2) - 91091/(64*(1 - 2*x)) - (14031*x)/16 - (6345*x^2)/32 -
(225*x^3)/8 - (39977*Log[1 - 2*x])/32

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Rubi [A]  time = 0.0696069, antiderivative size = 52, 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 \[ -\frac{225 x^3}{8}-\frac{6345 x^2}{32}-\frac{14031 x}{16}-\frac{91091}{64 (1-2 x)}+\frac{41503}{128 (1-2 x)^2}-\frac{39977}{32} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

41503/(128*(1 - 2*x)^2) - 91091/(64*(1 - 2*x)) - (14031*x)/16 - (6345*x^2)/32 -
(225*x^3)/8 - (39977*Log[1 - 2*x])/32

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{225 x^{3}}{8} - \frac{39977 \log{\left (- 2 x + 1 \right )}}{32} + \int \left (- \frac{14031}{16}\right )\, dx - \frac{6345 \int x\, dx}{16} - \frac{91091}{64 \left (- 2 x + 1\right )} + \frac{41503}{128 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x**3/8 - 39977*log(-2*x + 1)/32 + Integral(-14031/16, x) - 6345*Integral(x,
x)/16 - 91091/(64*(-2*x + 1)) + 41503/(128*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0316028, size = 47, normalized size = 0.9 \[ \frac{1}{32} \left (-\frac{2 \left (1800 x^5+10890 x^4+43884 x^3-84411 x^2-55 x+9720\right )}{(1-2 x)^2}-39977 \log (1-2 x)\right ) \]

Antiderivative was successfully verified.

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

[Out]

((-2*(9720 - 55*x - 84411*x^2 + 43884*x^3 + 10890*x^4 + 1800*x^5))/(1 - 2*x)^2 -
39977*Log[1 - 2*x])/32

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Maple [A]  time = 0.01, size = 41, normalized size = 0.8 \[ -{\frac{225\,{x}^{3}}{8}}-{\frac{6345\,{x}^{2}}{32}}-{\frac{14031\,x}{16}}+{\frac{41503}{128\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{91091}{-64+128\,x}}-{\frac{39977\,\ln \left ( -1+2\,x \right ) }{32}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/8*x^3-6345/32*x^2-14031/16*x+41503/128/(-1+2*x)^2+91091/64/(-1+2*x)-39977/3
2*ln(-1+2*x)

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Maxima [A]  time = 1.36248, size = 55, normalized size = 1.06 \[ -\frac{225}{8} \, x^{3} - \frac{6345}{32} \, x^{2} - \frac{14031}{16} \, x + \frac{539 \,{\left (676 \, x - 261\right )}}{128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{39977}{32} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/8*x^3 - 6345/32*x^2 - 14031/16*x + 539/128*(676*x - 261)/(4*x^2 - 4*x + 1)
- 39977/32*log(2*x - 1)

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Fricas [A]  time = 0.209763, size = 77, normalized size = 1.48 \[ -\frac{14400 \, x^{5} + 87120 \, x^{4} + 351072 \, x^{3} - 423612 \, x^{2} + 159908 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 252116 \, x + 140679}{128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/128*(14400*x^5 + 87120*x^4 + 351072*x^3 - 423612*x^2 + 159908*(4*x^2 - 4*x +
1)*log(2*x - 1) - 252116*x + 140679)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.29878, size = 42, normalized size = 0.81 \[ - \frac{225 x^{3}}{8} - \frac{6345 x^{2}}{32} - \frac{14031 x}{16} + \frac{364364 x - 140679}{512 x^{2} - 512 x + 128} - \frac{39977 \log{\left (2 x - 1 \right )}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x**3/8 - 6345*x**2/32 - 14031*x/16 + (364364*x - 140679)/(512*x**2 - 512*x
+ 128) - 39977*log(2*x - 1)/32

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GIAC/XCAS [A]  time = 0.206924, size = 50, normalized size = 0.96 \[ -\frac{225}{8} \, x^{3} - \frac{6345}{32} \, x^{2} - \frac{14031}{16} \, x + \frac{539 \,{\left (676 \, x - 261\right )}}{128 \,{\left (2 \, x - 1\right )}^{2}} - \frac{39977}{32} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/8*x^3 - 6345/32*x^2 - 14031/16*x + 539/128*(676*x - 261)/(2*x - 1)^2 - 3997
7/32*ln(abs(2*x - 1))