3.1278 \(\int \frac{(1-2 x)^2 (2+3 x)}{3+5 x} \, dx\)

Optimal. Leaf size=30 \[ \frac{4 x^3}{5}-\frac{28 x^2}{25}+\frac{43 x}{125}+\frac{121}{625} \log (5 x+3) \]

[Out]

(43*x)/125 - (28*x^2)/25 + (4*x^3)/5 + (121*Log[3 + 5*x])/625

_______________________________________________________________________________________

Rubi [A]  time = 0.0312799, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{4 x^3}{5}-\frac{28 x^2}{25}+\frac{43 x}{125}+\frac{121}{625} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(43*x)/125 - (28*x^2)/25 + (4*x^3)/5 + (121*Log[3 + 5*x])/625

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{4 x^{3}}{5} + \frac{121 \log{\left (5 x + 3 \right )}}{625} + \int \frac{43}{125}\, dx - \frac{56 \int x\, dx}{25} \]

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]

4*x**3/5 + 121*log(5*x + 3)/625 + Integral(43/125, x) - 56*Integral(x, x)/25

_______________________________________________________________________________________

Mathematica [A]  time = 0.0157787, size = 27, normalized size = 0.9 \[ \frac{1}{625} \left (500 x^3-700 x^2+215 x+121 \log (5 x+3)+489\right ) \]

Antiderivative was successfully verified.

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

[Out]

(489 + 215*x - 700*x^2 + 500*x^3 + 121*Log[3 + 5*x])/625

_______________________________________________________________________________________

Maple [A]  time = 0.005, size = 23, normalized size = 0.8 \[{\frac{43\,x}{125}}-{\frac{28\,{x}^{2}}{25}}+{\frac{4\,{x}^{3}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

43/125*x-28/25*x^2+4/5*x^3+121/625*ln(3+5*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.35114, size = 30, normalized size = 1. \[ \frac{4}{5} \, x^{3} - \frac{28}{25} \, x^{2} + \frac{43}{125} \, x + \frac{121}{625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/5*x^3 - 28/25*x^2 + 43/125*x + 121/625*log(5*x + 3)

_______________________________________________________________________________________

Fricas [A]  time = 0.212832, size = 30, normalized size = 1. \[ \frac{4}{5} \, x^{3} - \frac{28}{25} \, x^{2} + \frac{43}{125} \, x + \frac{121}{625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/5*x^3 - 28/25*x^2 + 43/125*x + 121/625*log(5*x + 3)

_______________________________________________________________________________________

Sympy [A]  time = 0.151231, size = 27, normalized size = 0.9 \[ \frac{4 x^{3}}{5} - \frac{28 x^{2}}{25} + \frac{43 x}{125} + \frac{121 \log{\left (5 x + 3 \right )}}{625} \]

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**3/5 - 28*x**2/25 + 43*x/125 + 121*log(5*x + 3)/625

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.20628, size = 31, normalized size = 1.03 \[ \frac{4}{5} \, x^{3} - \frac{28}{25} \, x^{2} + \frac{43}{125} \, x + \frac{121}{625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4/5*x^3 - 28/25*x^2 + 43/125*x + 121/625*ln(abs(5*x + 3))