3.1635 \(\int \frac{(3+5 x)^2}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=33 \[ -\frac{55}{4 (1-2 x)}+\frac{121}{16 (1-2 x)^2}-\frac{25}{8} \log (1-2 x) \]

[Out]

121/(16*(1 - 2*x)^2) - 55/(4*(1 - 2*x)) - (25*Log[1 - 2*x])/8

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Rubi [A]  time = 0.0319977, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{55}{4 (1-2 x)}+\frac{121}{16 (1-2 x)^2}-\frac{25}{8} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^2/(1 - 2*x)^3,x]

[Out]

121/(16*(1 - 2*x)^2) - 55/(4*(1 - 2*x)) - (25*Log[1 - 2*x])/8

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Rubi in Sympy [A]  time = 5.94066, size = 26, normalized size = 0.79 \[ - \frac{25 \log{\left (- 2 x + 1 \right )}}{8} - \frac{55}{4 \left (- 2 x + 1\right )} + \frac{121}{16 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-25*log(-2*x + 1)/8 - 55/(4*(-2*x + 1)) + 121/(16*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0130319, size = 33, normalized size = 1. \[ -\frac{55}{4 (1-2 x)}+\frac{121}{16 (1-2 x)^2}-\frac{25}{8} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

121/(16*(1 - 2*x)^2) - 55/(4*(1 - 2*x)) - (25*Log[1 - 2*x])/8

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Maple [A]  time = 0.008, size = 28, normalized size = 0.9 \[{\frac{121}{16\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{55}{-4+8\,x}}-{\frac{25\,\ln \left ( -1+2\,x \right ) }{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^2/(1-2*x)^3,x)

[Out]

121/16/(-1+2*x)^2+55/4/(-1+2*x)-25/8*ln(-1+2*x)

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Maxima [A]  time = 1.3362, size = 38, normalized size = 1.15 \[ \frac{11 \,{\left (40 \, x - 9\right )}}{16 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{25}{8} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

11/16*(40*x - 9)/(4*x^2 - 4*x + 1) - 25/8*log(2*x - 1)

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Fricas [A]  time = 0.214608, size = 50, normalized size = 1.52 \[ -\frac{50 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 440 \, x + 99}{16 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/16*(50*(4*x^2 - 4*x + 1)*log(2*x - 1) - 440*x + 99)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.254179, size = 24, normalized size = 0.73 \[ \frac{440 x - 99}{64 x^{2} - 64 x + 16} - \frac{25 \log{\left (2 x - 1 \right )}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(440*x - 99)/(64*x**2 - 64*x + 16) - 25*log(2*x - 1)/8

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GIAC/XCAS [A]  time = 0.208236, size = 32, normalized size = 0.97 \[ \frac{11 \,{\left (40 \, x - 9\right )}}{16 \,{\left (2 \, x - 1\right )}^{2}} - \frac{25}{8} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

11/16*(40*x - 9)/(2*x - 1)^2 - 25/8*ln(abs(2*x - 1))