3.1620 \(\int \frac{(2+3 x) (3+5 x)}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=33 \[ -\frac{17}{2 (1-2 x)}+\frac{77}{16 (1-2 x)^2}-\frac{15}{8} \log (1-2 x) \]

[Out]

77/(16*(1 - 2*x)^2) - 17/(2*(1 - 2*x)) - (15*Log[1 - 2*x])/8

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Rubi [A]  time = 0.0357488, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{17}{2 (1-2 x)}+\frac{77}{16 (1-2 x)^2}-\frac{15}{8} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

77/(16*(1 - 2*x)^2) - 17/(2*(1 - 2*x)) - (15*Log[1 - 2*x])/8

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Rubi in Sympy [A]  time = 6.66805, size = 26, normalized size = 0.79 \[ - \frac{15 \log{\left (- 2 x + 1 \right )}}{8} - \frac{17}{2 \left (- 2 x + 1\right )} + \frac{77}{16 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15*log(-2*x + 1)/8 - 17/(2*(-2*x + 1)) + 77/(16*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0113085, size = 33, normalized size = 1. \[ -\frac{17}{2 (1-2 x)}+\frac{77}{16 (1-2 x)^2}-\frac{15}{8} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

77/(16*(1 - 2*x)^2) - 17/(2*(1 - 2*x)) - (15*Log[1 - 2*x])/8

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Maple [A]  time = 0.008, size = 28, normalized size = 0.9 \[{\frac{77}{16\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{17}{-2+4\,x}}-{\frac{15\,\ln \left ( -1+2\,x \right ) }{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

77/16/(-1+2*x)^2+17/2/(-1+2*x)-15/8*ln(-1+2*x)

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Maxima [A]  time = 1.32232, size = 38, normalized size = 1.15 \[ \frac{272 \, x - 59}{16 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{15}{8} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/16*(272*x - 59)/(4*x^2 - 4*x + 1) - 15/8*log(2*x - 1)

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Fricas [A]  time = 0.206237, size = 50, normalized size = 1.52 \[ -\frac{30 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 272 \, x + 59}{16 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/16*(30*(4*x^2 - 4*x + 1)*log(2*x - 1) - 272*x + 59)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.248833, size = 24, normalized size = 0.73 \[ \frac{272 x - 59}{64 x^{2} - 64 x + 16} - \frac{15 \log{\left (2 x - 1 \right )}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(272*x - 59)/(64*x**2 - 64*x + 16) - 15*log(2*x - 1)/8

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GIAC/XCAS [A]  time = 0.211121, size = 32, normalized size = 0.97 \[ \frac{272 \, x - 59}{16 \,{\left (2 \, x - 1\right )}^{2}} - \frac{15}{8} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/16*(272*x - 59)/(2*x - 1)^2 - 15/8*ln(abs(2*x - 1))