3.1211 \(\int \frac{(1-2 x) (2+3 x)}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=33 \[ -\frac{31}{125 (5 x+3)}-\frac{11}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3) \]

[Out]

-11/(250*(3 + 5*x)^2) - 31/(125*(3 + 5*x)) - (6*Log[3 + 5*x])/125

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Rubi [A]  time = 0.0350468, 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 \[ -\frac{31}{125 (5 x+3)}-\frac{11}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-11/(250*(3 + 5*x)^2) - 31/(125*(3 + 5*x)) - (6*Log[3 + 5*x])/125

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Rubi in Sympy [A]  time = 6.10584, size = 27, normalized size = 0.82 \[ - \frac{6 \log{\left (5 x + 3 \right )}}{125} - \frac{31}{125 \left (5 x + 3\right )} - \frac{11}{250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6*log(5*x + 3)/125 - 31/(125*(5*x + 3)) - 11/(250*(5*x + 3)**2)

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Mathematica [A]  time = 0.0123171, size = 33, normalized size = 1. \[ -\frac{31}{125 (5 x+3)}-\frac{11}{250 (5 x+3)^2}-\frac{6}{125} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-11/(250*(3 + 5*x)^2) - 31/(125*(3 + 5*x)) - (6*Log[3 + 5*x])/125

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Maple [A]  time = 0.008, size = 28, normalized size = 0.9 \[ -{\frac{11}{250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{31}{375+625\,x}}-{\frac{6\,\ln \left ( 3+5\,x \right ) }{125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-11/250/(3+5*x)^2-31/125/(3+5*x)-6/125*ln(3+5*x)

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Maxima [A]  time = 1.35184, size = 38, normalized size = 1.15 \[ -\frac{310 \, x + 197}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac{6}{125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/250*(310*x + 197)/(25*x^2 + 30*x + 9) - 6/125*log(5*x + 3)

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Fricas [A]  time = 0.226339, size = 50, normalized size = 1.52 \[ -\frac{12 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 310 \, x + 197}{250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/250*(12*(25*x^2 + 30*x + 9)*log(5*x + 3) + 310*x + 197)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.243395, size = 26, normalized size = 0.79 \[ - \frac{310 x + 197}{6250 x^{2} + 7500 x + 2250} - \frac{6 \log{\left (5 x + 3 \right )}}{125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(310*x + 197)/(6250*x**2 + 7500*x + 2250) - 6*log(5*x + 3)/125

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GIAC/XCAS [A]  time = 0.207319, size = 32, normalized size = 0.97 \[ -\frac{310 \, x + 197}{250 \,{\left (5 \, x + 3\right )}^{2}} - \frac{6}{125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/250*(310*x + 197)/(5*x + 3)^2 - 6/125*ln(abs(5*x + 3))