3.1543 \(\int \frac{(2+3 x)^2 (3+5 x)^2}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=41 \[ \frac{75 x^3}{4}+\frac{795 x^2}{8}+\frac{5119 x}{16}+\frac{5929}{32 (1-2 x)}+\frac{1309}{4} \log (1-2 x) \]

[Out]

5929/(32*(1 - 2*x)) + (5119*x)/16 + (795*x^2)/8 + (75*x^3)/4 + (1309*Log[1 - 2*x
])/4

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Rubi [A]  time = 0.0604726, antiderivative size = 41, 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 \[ \frac{75 x^3}{4}+\frac{795 x^2}{8}+\frac{5119 x}{16}+\frac{5929}{32 (1-2 x)}+\frac{1309}{4} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

5929/(32*(1 - 2*x)) + (5119*x)/16 + (795*x^2)/8 + (75*x^3)/4 + (1309*Log[1 - 2*x
])/4

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{75 x^{3}}{4} + \frac{1309 \log{\left (- 2 x + 1 \right )}}{4} + \int \frac{5119}{16}\, dx + \frac{795 \int x\, dx}{4} + \frac{5929}{32 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75*x**3/4 + 1309*log(-2*x + 1)/4 + Integral(5119/16, x) + 795*Integral(x, x)/4 +
5929/(32*(-2*x + 1))

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Mathematica [A]  time = 0.0243373, size = 41, normalized size = 1. \[ \frac{300 x^4+1440 x^3+4324 x^2-5554 x+2618 (2 x-1) \log (1-2 x)+15}{16 x-8} \]

Antiderivative was successfully verified.

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

[Out]

(15 - 5554*x + 4324*x^2 + 1440*x^3 + 300*x^4 + 2618*(-1 + 2*x)*Log[1 - 2*x])/(-8
+ 16*x)

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Maple [A]  time = 0.008, size = 32, normalized size = 0.8 \[{\frac{75\,{x}^{3}}{4}}+{\frac{795\,{x}^{2}}{8}}+{\frac{5119\,x}{16}}-{\frac{5929}{-32+64\,x}}+{\frac{1309\,\ln \left ( -1+2\,x \right ) }{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75/4*x^3+795/8*x^2+5119/16*x-5929/32/(-1+2*x)+1309/4*ln(-1+2*x)

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Maxima [A]  time = 1.35785, size = 42, normalized size = 1.02 \[ \frac{75}{4} \, x^{3} + \frac{795}{8} \, x^{2} + \frac{5119}{16} \, x - \frac{5929}{32 \,{\left (2 \, x - 1\right )}} + \frac{1309}{4} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75/4*x^3 + 795/8*x^2 + 5119/16*x - 5929/32/(2*x - 1) + 1309/4*log(2*x - 1)

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Fricas [A]  time = 0.204143, size = 57, normalized size = 1.39 \[ \frac{1200 \, x^{4} + 5760 \, x^{3} + 17296 \, x^{2} + 10472 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 10238 \, x - 5929}{32 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/32*(1200*x^4 + 5760*x^3 + 17296*x^2 + 10472*(2*x - 1)*log(2*x - 1) - 10238*x -
5929)/(2*x - 1)

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Sympy [A]  time = 0.202696, size = 34, normalized size = 0.83 \[ \frac{75 x^{3}}{4} + \frac{795 x^{2}}{8} + \frac{5119 x}{16} + \frac{1309 \log{\left (2 x - 1 \right )}}{4} - \frac{5929}{64 x - 32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

75*x**3/4 + 795*x**2/8 + 5119*x/16 + 1309*log(2*x - 1)/4 - 5929/(64*x - 32)

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GIAC/XCAS [A]  time = 0.219024, size = 77, normalized size = 1.88 \[ \frac{1}{32} \,{\left (2 \, x - 1\right )}^{3}{\left (\frac{1020}{2 \, x - 1} + \frac{6934}{{\left (2 \, x - 1\right )}^{2}} + 75\right )} - \frac{5929}{32 \,{\left (2 \, x - 1\right )}} - \frac{1309}{4} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/32*(2*x - 1)^3*(1020/(2*x - 1) + 6934/(2*x - 1)^2 + 75) - 5929/32/(2*x - 1) -
1309/4*ln(1/2*abs(2*x - 1)/(2*x - 1)^2)