3.1297 \(\int \frac{(1-2 x)^2}{(2+3 x)^2 (3+5 x)^2} \, dx\)

Optimal. Leaf size=39 \[ -\frac{49}{3 (3 x+2)}-\frac{121}{5 (5 x+3)}+154 \log (3 x+2)-154 \log (5 x+3) \]

[Out]

-49/(3*(2 + 3*x)) - 121/(5*(3 + 5*x)) + 154*Log[2 + 3*x] - 154*Log[3 + 5*x]

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Rubi [A]  time = 0.050773, antiderivative size = 39, 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 \[ -\frac{49}{3 (3 x+2)}-\frac{121}{5 (5 x+3)}+154 \log (3 x+2)-154 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-49/(3*(2 + 3*x)) - 121/(5*(3 + 5*x)) + 154*Log[2 + 3*x] - 154*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 7.23411, size = 29, normalized size = 0.74 \[ 154 \log{\left (3 x + 2 \right )} - 154 \log{\left (5 x + 3 \right )} - \frac{121}{5 \left (5 x + 3\right )} - \frac{49}{3 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

154*log(3*x + 2) - 154*log(5*x + 3) - 121/(5*(5*x + 3)) - 49/(3*(3*x + 2))

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Mathematica [A]  time = 0.051059, size = 61, normalized size = 1.56 \[ -\frac{-2310 \left (15 x^2+19 x+6\right ) \log (5 (3 x+2))+2310 \left (15 x^2+19 x+6\right ) \log (5 x+3)+2314 x+1461}{15 (3 x+2) (5 x+3)} \]

Antiderivative was successfully verified.

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

[Out]

-(1461 + 2314*x - 2310*(6 + 19*x + 15*x^2)*Log[5*(2 + 3*x)] + 2310*(6 + 19*x + 1
5*x^2)*Log[3 + 5*x])/(15*(2 + 3*x)*(3 + 5*x))

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Maple [A]  time = 0.013, size = 36, normalized size = 0.9 \[ -{\frac{49}{6+9\,x}}-{\frac{121}{15+25\,x}}+154\,\ln \left ( 2+3\,x \right ) -154\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-49/3/(2+3*x)-121/5/(3+5*x)+154*ln(2+3*x)-154*ln(3+5*x)

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Maxima [A]  time = 1.34584, size = 49, normalized size = 1.26 \[ -\frac{2314 \, x + 1461}{15 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} - 154 \, \log \left (5 \, x + 3\right ) + 154 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/15*(2314*x + 1461)/(15*x^2 + 19*x + 6) - 154*log(5*x + 3) + 154*log(3*x + 2)

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Fricas [A]  time = 0.213942, size = 74, normalized size = 1.9 \[ -\frac{2310 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 2310 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 2314 \, x + 1461}{15 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/15*(2310*(15*x^2 + 19*x + 6)*log(5*x + 3) - 2310*(15*x^2 + 19*x + 6)*log(3*x
+ 2) + 2314*x + 1461)/(15*x^2 + 19*x + 6)

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Sympy [A]  time = 0.330654, size = 31, normalized size = 0.79 \[ - \frac{2314 x + 1461}{225 x^{2} + 285 x + 90} - 154 \log{\left (x + \frac{3}{5} \right )} + 154 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(2314*x + 1461)/(225*x**2 + 285*x + 90) - 154*log(x + 3/5) + 154*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.212463, size = 51, normalized size = 1.31 \[ -\frac{121}{5 \,{\left (5 \, x + 3\right )}} + \frac{245}{\frac{1}{5 \, x + 3} + 3} + 154 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-121/5/(5*x + 3) + 245/(1/(5*x + 3) + 3) + 154*ln(abs(-1/(5*x + 3) - 3))