3.1177 \(\int \frac{(1-2 x) (2+3 x)^5}{3+5 x} \, dx\)

Optimal. Leaf size=51 \[ -\frac{81 x^6}{5}-\frac{5427 x^5}{125}-\frac{17469 x^4}{500}+\frac{2469 x^3}{625}+\frac{127779 x^2}{6250}+\frac{166663 x}{15625}+\frac{11 \log (5 x+3)}{78125} \]

[Out]

(166663*x)/15625 + (127779*x^2)/6250 + (2469*x^3)/625 - (17469*x^4)/500 - (5427*
x^5)/125 - (81*x^6)/5 + (11*Log[3 + 5*x])/78125

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Rubi [A]  time = 0.0466561, antiderivative size = 51, 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 \[ -\frac{81 x^6}{5}-\frac{5427 x^5}{125}-\frac{17469 x^4}{500}+\frac{2469 x^3}{625}+\frac{127779 x^2}{6250}+\frac{166663 x}{15625}+\frac{11 \log (5 x+3)}{78125} \]

Antiderivative was successfully verified.

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

[Out]

(166663*x)/15625 + (127779*x^2)/6250 + (2469*x^3)/625 - (17469*x^4)/500 - (5427*
x^5)/125 - (81*x^6)/5 + (11*Log[3 + 5*x])/78125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{81 x^{6}}{5} - \frac{5427 x^{5}}{125} - \frac{17469 x^{4}}{500} + \frac{2469 x^{3}}{625} + \frac{11 \log{\left (5 x + 3 \right )}}{78125} + \int \frac{166663}{15625}\, dx + \frac{127779 \int x\, dx}{3125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81*x**6/5 - 5427*x**5/125 - 17469*x**4/500 + 2469*x**3/625 + 11*log(5*x + 3)/78
125 + Integral(166663/15625, x) + 127779*Integral(x, x)/3125

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Mathematica [A]  time = 0.0201832, size = 42, normalized size = 0.82 \[ \frac{-25312500 x^6-67837500 x^5-54590625 x^4+6172500 x^3+31944750 x^2+16666300 x+220 \log (5 x+3)+2813811}{1562500} \]

Antiderivative was successfully verified.

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

[Out]

(2813811 + 16666300*x + 31944750*x^2 + 6172500*x^3 - 54590625*x^4 - 67837500*x^5
- 25312500*x^6 + 220*Log[3 + 5*x])/1562500

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Maple [A]  time = 0.004, size = 38, normalized size = 0.8 \[{\frac{166663\,x}{15625}}+{\frac{127779\,{x}^{2}}{6250}}+{\frac{2469\,{x}^{3}}{625}}-{\frac{17469\,{x}^{4}}{500}}-{\frac{5427\,{x}^{5}}{125}}-{\frac{81\,{x}^{6}}{5}}+{\frac{11\,\ln \left ( 3+5\,x \right ) }{78125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

166663/15625*x+127779/6250*x^2+2469/625*x^3-17469/500*x^4-5427/125*x^5-81/5*x^6+
11/78125*ln(3+5*x)

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Maxima [A]  time = 1.32368, size = 50, normalized size = 0.98 \[ -\frac{81}{5} \, x^{6} - \frac{5427}{125} \, x^{5} - \frac{17469}{500} \, x^{4} + \frac{2469}{625} \, x^{3} + \frac{127779}{6250} \, x^{2} + \frac{166663}{15625} \, x + \frac{11}{78125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81/5*x^6 - 5427/125*x^5 - 17469/500*x^4 + 2469/625*x^3 + 127779/6250*x^2 + 1666
63/15625*x + 11/78125*log(5*x + 3)

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Fricas [A]  time = 0.215198, size = 50, normalized size = 0.98 \[ -\frac{81}{5} \, x^{6} - \frac{5427}{125} \, x^{5} - \frac{17469}{500} \, x^{4} + \frac{2469}{625} \, x^{3} + \frac{127779}{6250} \, x^{2} + \frac{166663}{15625} \, x + \frac{11}{78125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81/5*x^6 - 5427/125*x^5 - 17469/500*x^4 + 2469/625*x^3 + 127779/6250*x^2 + 1666
63/15625*x + 11/78125*log(5*x + 3)

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Sympy [A]  time = 0.18775, size = 48, normalized size = 0.94 \[ - \frac{81 x^{6}}{5} - \frac{5427 x^{5}}{125} - \frac{17469 x^{4}}{500} + \frac{2469 x^{3}}{625} + \frac{127779 x^{2}}{6250} + \frac{166663 x}{15625} + \frac{11 \log{\left (5 x + 3 \right )}}{78125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81*x**6/5 - 5427*x**5/125 - 17469*x**4/500 + 2469*x**3/625 + 127779*x**2/6250 +
166663*x/15625 + 11*log(5*x + 3)/78125

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GIAC/XCAS [A]  time = 0.208612, size = 51, normalized size = 1. \[ -\frac{81}{5} \, x^{6} - \frac{5427}{125} \, x^{5} - \frac{17469}{500} \, x^{4} + \frac{2469}{625} \, x^{3} + \frac{127779}{6250} \, x^{2} + \frac{166663}{15625} \, x + \frac{11}{78125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-81/5*x^6 - 5427/125*x^5 - 17469/500*x^4 + 2469/625*x^3 + 127779/6250*x^2 + 1666
63/15625*x + 11/78125*ln(abs(5*x + 3))