3.1280 \(\int \frac{(1-2 x)^2}{(2+3 x) (3+5 x)} \, dx\)

Optimal. Leaf size=26 \[ \frac{4 x}{15}-\frac{49}{9} \log (3 x+2)+\frac{121}{25} \log (5 x+3) \]

[Out]

(4*x)/15 - (49*Log[2 + 3*x])/9 + (121*Log[3 + 5*x])/25

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Rubi [A]  time = 0.0379807, 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 \[ \frac{4 x}{15}-\frac{49}{9} \log (3 x+2)+\frac{121}{25} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(4*x)/15 - (49*Log[2 + 3*x])/9 + (121*Log[3 + 5*x])/25

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{49 \log{\left (3 x + 2 \right )}}{9} + \frac{121 \log{\left (5 x + 3 \right )}}{25} + \int \frac{4}{15}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-49*log(3*x + 2)/9 + 121*log(5*x + 3)/25 + Integral(4/15, x)

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Mathematica [A]  time = 0.016283, size = 27, normalized size = 1.04 \[ \frac{1}{225} (60 x-1225 \log (3 x+2)+1089 \log (-3 (5 x+3))+40) \]

Antiderivative was successfully verified.

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

[Out]

(40 + 60*x - 1225*Log[2 + 3*x] + 1089*Log[-3*(3 + 5*x)])/225

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Maple [A]  time = 0.009, size = 21, normalized size = 0.8 \[{\frac{4\,x}{15}}-{\frac{49\,\ln \left ( 2+3\,x \right ) }{9}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{25}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/15*x-49/9*ln(2+3*x)+121/25*ln(3+5*x)

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Maxima [A]  time = 1.34716, size = 27, normalized size = 1.04 \[ \frac{4}{15} \, x + \frac{121}{25} \, \log \left (5 \, x + 3\right ) - \frac{49}{9} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/15*x + 121/25*log(5*x + 3) - 49/9*log(3*x + 2)

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Fricas [A]  time = 0.20753, size = 27, normalized size = 1.04 \[ \frac{4}{15} \, x + \frac{121}{25} \, \log \left (5 \, x + 3\right ) - \frac{49}{9} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/15*x + 121/25*log(5*x + 3) - 49/9*log(3*x + 2)

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Sympy [A]  time = 0.24982, size = 24, normalized size = 0.92 \[ \frac{4 x}{15} + \frac{121 \log{\left (x + \frac{3}{5} \right )}}{25} - \frac{49 \log{\left (x + \frac{2}{3} \right )}}{9} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4*x/15 + 121*log(x + 3/5)/25 - 49*log(x + 2/3)/9

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GIAC/XCAS [A]  time = 0.209862, size = 30, normalized size = 1.15 \[ \frac{4}{15} \, x + \frac{121}{25} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{49}{9} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/15*x + 121/25*ln(abs(5*x + 3)) - 49/9*ln(abs(3*x + 2))