3.1474 \(\int \frac{(2+3 x)^2}{(1-2 x) (3+5 x)} \, dx\)

Optimal. Leaf size=26 \[ -\frac{9 x}{10}-\frac{49}{44} \log (1-2 x)+\frac{1}{275} \log (5 x+3) \]

[Out]

(-9*x)/10 - (49*Log[1 - 2*x])/44 + Log[3 + 5*x]/275

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Rubi [A]  time = 0.039115, antiderivative size = 26, 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 \[ -\frac{9 x}{10}-\frac{49}{44} \log (1-2 x)+\frac{1}{275} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(-9*x)/10 - (49*Log[1 - 2*x])/44 + Log[3 + 5*x]/275

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{49 \log{\left (- 2 x + 1 \right )}}{44} + \frac{\log{\left (5 x + 3 \right )}}{275} + \int \left (- \frac{9}{10}\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-49*log(-2*x + 1)/44 + log(5*x + 3)/275 + Integral(-9/10, x)

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Mathematica [A]  time = 0.0191167, size = 31, normalized size = 1.19 \[ -\frac{9 x}{10}-\frac{49}{44} \log (3-6 x)+\frac{1}{275} \log (-3 (5 x+3))-\frac{3}{5} \]

Antiderivative was successfully verified.

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

[Out]

-3/5 - (9*x)/10 - (49*Log[3 - 6*x])/44 + Log[-3*(3 + 5*x)]/275

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Maple [A]  time = 0.009, size = 21, normalized size = 0.8 \[ -{\frac{9\,x}{10}}+{\frac{\ln \left ( 3+5\,x \right ) }{275}}-{\frac{49\,\ln \left ( -1+2\,x \right ) }{44}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-9/10*x+1/275*ln(3+5*x)-49/44*ln(-1+2*x)

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Maxima [A]  time = 1.35001, size = 27, normalized size = 1.04 \[ -\frac{9}{10} \, x + \frac{1}{275} \, \log \left (5 \, x + 3\right ) - \frac{49}{44} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-9/10*x + 1/275*log(5*x + 3) - 49/44*log(2*x - 1)

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Fricas [A]  time = 0.210937, size = 27, normalized size = 1.04 \[ -\frac{9}{10} \, x + \frac{1}{275} \, \log \left (5 \, x + 3\right ) - \frac{49}{44} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-9/10*x + 1/275*log(5*x + 3) - 49/44*log(2*x - 1)

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Sympy [A]  time = 0.274041, size = 22, normalized size = 0.85 \[ - \frac{9 x}{10} - \frac{49 \log{\left (x - \frac{1}{2} \right )}}{44} + \frac{\log{\left (x + \frac{3}{5} \right )}}{275} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-9*x/10 - 49*log(x - 1/2)/44 + log(x + 3/5)/275

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GIAC/XCAS [A]  time = 0.207343, size = 30, normalized size = 1.15 \[ -\frac{9}{10} \, x + \frac{1}{275} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{49}{44} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-9/10*x + 1/275*ln(abs(5*x + 3)) - 49/44*ln(abs(2*x - 1))