3.1279 \(\int \frac{(1-2 x)^2}{3+5 x} \, dx\)

Optimal. Leaf size=23 \[ \frac{2 x^2}{5}-\frac{32 x}{25}+\frac{121}{125} \log (5 x+3) \]

[Out]

(-32*x)/25 + (2*x^2)/5 + (121*Log[3 + 5*x])/125

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Rubi [A]  time = 0.0217076, antiderivative size = 23, 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 \[ \frac{2 x^2}{5}-\frac{32 x}{25}+\frac{121}{125} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2/(3 + 5*x),x]

[Out]

(-32*x)/25 + (2*x^2)/5 + (121*Log[3 + 5*x])/125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{121 \log{\left (5 x + 3 \right )}}{125} + \int \left (- \frac{32}{25}\right )\, dx + \frac{4 \int x\, dx}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

121*log(5*x + 3)/125 + Integral(-32/25, x) + 4*Integral(x, x)/5

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Mathematica [A]  time = 0.00856435, size = 22, normalized size = 0.96 \[ \frac{1}{125} \left (50 x^2-160 x+121 \log (5 x+3)-114\right ) \]

Antiderivative was successfully verified.

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

[Out]

(-114 - 160*x + 50*x^2 + 121*Log[3 + 5*x])/125

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Maple [A]  time = 0.003, size = 18, normalized size = 0.8 \[ -{\frac{32\,x}{25}}+{\frac{2\,{x}^{2}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{125}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2/(3+5*x),x)

[Out]

-32/25*x+2/5*x^2+121/125*ln(3+5*x)

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Maxima [A]  time = 1.35199, size = 23, normalized size = 1. \[ \frac{2}{5} \, x^{2} - \frac{32}{25} \, x + \frac{121}{125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/5*x^2 - 32/25*x + 121/125*log(5*x + 3)

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Fricas [A]  time = 0.209169, size = 23, normalized size = 1. \[ \frac{2}{5} \, x^{2} - \frac{32}{25} \, x + \frac{121}{125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/5*x^2 - 32/25*x + 121/125*log(5*x + 3)

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Sympy [A]  time = 0.131266, size = 20, normalized size = 0.87 \[ \frac{2 x^{2}}{5} - \frac{32 x}{25} + \frac{121 \log{\left (5 x + 3 \right )}}{125} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2/(3+5*x),x)

[Out]

2*x**2/5 - 32*x/25 + 121*log(5*x + 3)/125

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GIAC/XCAS [A]  time = 0.212493, size = 24, normalized size = 1.04 \[ \frac{2}{5} \, x^{2} - \frac{32}{25} \, x + \frac{121}{125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/5*x^2 - 32/25*x + 121/125*ln(abs(5*x + 3))