3.1542 \(\int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=48 \[ \frac{675 x^4}{16}+\frac{945 x^3}{4}+\frac{21717 x^2}{32}+\frac{12973 x}{8}+\frac{41503}{64 (1-2 x)}+\frac{91091}{64} \log (1-2 x) \]

[Out]

41503/(64*(1 - 2*x)) + (12973*x)/8 + (21717*x^2)/32 + (945*x^3)/4 + (675*x^4)/16
+ (91091*Log[1 - 2*x])/64

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Rubi [A]  time = 0.0641672, antiderivative size = 48, 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 \[ \frac{675 x^4}{16}+\frac{945 x^3}{4}+\frac{21717 x^2}{32}+\frac{12973 x}{8}+\frac{41503}{64 (1-2 x)}+\frac{91091}{64} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

41503/(64*(1 - 2*x)) + (12973*x)/8 + (21717*x^2)/32 + (945*x^3)/4 + (675*x^4)/16
+ (91091*Log[1 - 2*x])/64

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{675 x^{4}}{16} + \frac{945 x^{3}}{4} + \frac{91091 \log{\left (- 2 x + 1 \right )}}{64} + \int \frac{12973}{8}\, dx + \frac{21717 \int x\, dx}{16} + \frac{41503}{64 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675*x**4/16 + 945*x**3/4 + 91091*log(-2*x + 1)/64 + Integral(12973/8, x) + 21717
*Integral(x, x)/16 + 41503/(64*(-2*x + 1))

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Mathematica [A]  time = 0.023865, size = 49, normalized size = 1.02 \[ \frac{21600 x^5+110160 x^4+286992 x^3+656536 x^2-933610 x+364364 (2 x-1) \log (1-2 x)+93225}{256 (2 x-1)} \]

Antiderivative was successfully verified.

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

[Out]

(93225 - 933610*x + 656536*x^2 + 286992*x^3 + 110160*x^4 + 21600*x^5 + 364364*(-
1 + 2*x)*Log[1 - 2*x])/(256*(-1 + 2*x))

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Maple [A]  time = 0.009, size = 37, normalized size = 0.8 \[{\frac{675\,{x}^{4}}{16}}+{\frac{945\,{x}^{3}}{4}}+{\frac{21717\,{x}^{2}}{32}}+{\frac{12973\,x}{8}}-{\frac{41503}{-64+128\,x}}+{\frac{91091\,\ln \left ( -1+2\,x \right ) }{64}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/16*x^4+945/4*x^3+21717/32*x^2+12973/8*x-41503/64/(-1+2*x)+91091/64*ln(-1+2*x
)

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Maxima [A]  time = 1.33758, size = 49, normalized size = 1.02 \[ \frac{675}{16} \, x^{4} + \frac{945}{4} \, x^{3} + \frac{21717}{32} \, x^{2} + \frac{12973}{8} \, x - \frac{41503}{64 \,{\left (2 \, x - 1\right )}} + \frac{91091}{64} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/16*x^4 + 945/4*x^3 + 21717/32*x^2 + 12973/8*x - 41503/64/(2*x - 1) + 91091/6
4*log(2*x - 1)

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Fricas [A]  time = 0.205551, size = 63, normalized size = 1.31 \[ \frac{5400 \, x^{5} + 27540 \, x^{4} + 71748 \, x^{3} + 164134 \, x^{2} + 91091 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 103784 \, x - 41503}{64 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/64*(5400*x^5 + 27540*x^4 + 71748*x^3 + 164134*x^2 + 91091*(2*x - 1)*log(2*x -
1) - 103784*x - 41503)/(2*x - 1)

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Sympy [A]  time = 0.219413, size = 41, normalized size = 0.85 \[ \frac{675 x^{4}}{16} + \frac{945 x^{3}}{4} + \frac{21717 x^{2}}{32} + \frac{12973 x}{8} + \frac{91091 \log{\left (2 x - 1 \right )}}{64} - \frac{41503}{128 x - 64} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675*x**4/16 + 945*x**3/4 + 21717*x**2/32 + 12973*x/8 + 91091*log(2*x - 1)/64 - 4
1503/(128*x - 64)

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GIAC/XCAS [A]  time = 0.214989, size = 89, normalized size = 1.85 \[ \frac{1}{256} \,{\left (2 \, x - 1\right )}^{4}{\left (\frac{10260}{2 \, x - 1} + \frac{70164}{{\left (2 \, x - 1\right )}^{2}} + \frac{319816}{{\left (2 \, x - 1\right )}^{3}} + 675\right )} - \frac{41503}{64 \,{\left (2 \, x - 1\right )}} - \frac{91091}{64} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/256*(2*x - 1)^4*(10260/(2*x - 1) + 70164/(2*x - 1)^2 + 319816/(2*x - 1)^3 + 67
5) - 41503/64/(2*x - 1) - 91091/64*ln(1/2*abs(2*x - 1)/(2*x - 1)^2)