3.1633 \(\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=45 \[ -\frac{225 x^2}{16}-\frac{1815 x}{16}-\frac{1309}{4 (1-2 x)}+\frac{5929}{64 (1-2 x)^2}-\frac{3467}{16} \log (1-2 x) \]

[Out]

5929/(64*(1 - 2*x)^2) - 1309/(4*(1 - 2*x)) - (1815*x)/16 - (225*x^2)/16 - (3467*
Log[1 - 2*x])/16

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Rubi [A]  time = 0.063922, antiderivative size = 45, 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 \[ -\frac{225 x^2}{16}-\frac{1815 x}{16}-\frac{1309}{4 (1-2 x)}+\frac{5929}{64 (1-2 x)^2}-\frac{3467}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

5929/(64*(1 - 2*x)^2) - 1309/(4*(1 - 2*x)) - (1815*x)/16 - (225*x^2)/16 - (3467*
Log[1 - 2*x])/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{3467 \log{\left (- 2 x + 1 \right )}}{16} + \int \left (- \frac{1815}{16}\right )\, dx - \frac{225 \int x\, dx}{8} - \frac{1309}{4 \left (- 2 x + 1\right )} + \frac{5929}{64 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3467*log(-2*x + 1)/16 + Integral(-1815/16, x) - 225*Integral(x, x)/8 - 1309/(4*
(-2*x + 1)) + 5929/(64*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0252441, size = 46, normalized size = 1.02 \[ -\frac{900 x^4+6360 x^3-10890 x^2-4802 x+3467 (1-2 x)^2 \log (1-2 x)+2790}{16 (1-2 x)^2} \]

Antiderivative was successfully verified.

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

[Out]

-(2790 - 4802*x - 10890*x^2 + 6360*x^3 + 900*x^4 + 3467*(1 - 2*x)^2*Log[1 - 2*x]
)/(16*(1 - 2*x)^2)

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Maple [A]  time = 0.009, size = 36, normalized size = 0.8 \[ -{\frac{225\,{x}^{2}}{16}}-{\frac{1815\,x}{16}}+{\frac{5929}{64\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{1309}{-4+8\,x}}-{\frac{3467\,\ln \left ( -1+2\,x \right ) }{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/16*x^2-1815/16*x+5929/64/(-1+2*x)^2+1309/4/(-1+2*x)-3467/16*ln(-1+2*x)

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Maxima [A]  time = 1.33928, size = 49, normalized size = 1.09 \[ -\frac{225}{16} \, x^{2} - \frac{1815}{16} \, x + \frac{77 \,{\left (544 \, x - 195\right )}}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{3467}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/16*x^2 - 1815/16*x + 77/64*(544*x - 195)/(4*x^2 - 4*x + 1) - 3467/16*log(2*
x - 1)

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Fricas [A]  time = 0.214159, size = 70, normalized size = 1.56 \[ -\frac{3600 \, x^{4} + 25440 \, x^{3} - 28140 \, x^{2} + 13868 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 34628 \, x + 15015}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/64*(3600*x^4 + 25440*x^3 - 28140*x^2 + 13868*(4*x^2 - 4*x + 1)*log(2*x - 1) -
34628*x + 15015)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.285125, size = 36, normalized size = 0.8 \[ - \frac{225 x^{2}}{16} - \frac{1815 x}{16} + \frac{41888 x - 15015}{256 x^{2} - 256 x + 64} - \frac{3467 \log{\left (2 x - 1 \right )}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*x**2/16 - 1815*x/16 + (41888*x - 15015)/(256*x**2 - 256*x + 64) - 3467*log(
2*x - 1)/16

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GIAC/XCAS [A]  time = 0.206495, size = 43, normalized size = 0.96 \[ -\frac{225}{16} \, x^{2} - \frac{1815}{16} \, x + \frac{77 \,{\left (544 \, x - 195\right )}}{64 \,{\left (2 \, x - 1\right )}^{2}} - \frac{3467}{16} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/16*x^2 - 1815/16*x + 77/64*(544*x - 195)/(2*x - 1)^2 - 3467/16*ln(abs(2*x -
1))