3.1275 \(\int \frac{(1-2 x)^2 (2+3 x)^4}{3+5 x} \, dx\)

Optimal. Leaf size=51 \[ \frac{54 x^6}{5}+\frac{1728 x^5}{125}-\frac{3159 x^4}{500}-\frac{7841 x^3}{625}+\frac{5569 x^2}{6250}+\frac{83293 x}{15625}+\frac{121 \log (5 x+3)}{78125} \]

[Out]

(83293*x)/15625 + (5569*x^2)/6250 - (7841*x^3)/625 - (3159*x^4)/500 + (1728*x^5)
/125 + (54*x^6)/5 + (121*Log[3 + 5*x])/78125

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Rubi [A]  time = 0.0531409, antiderivative size = 51, 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 \[ \frac{54 x^6}{5}+\frac{1728 x^5}{125}-\frac{3159 x^4}{500}-\frac{7841 x^3}{625}+\frac{5569 x^2}{6250}+\frac{83293 x}{15625}+\frac{121 \log (5 x+3)}{78125} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x),x]

[Out]

(83293*x)/15625 + (5569*x^2)/6250 - (7841*x^3)/625 - (3159*x^4)/500 + (1728*x^5)
/125 + (54*x^6)/5 + (121*Log[3 + 5*x])/78125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{54 x^{6}}{5} + \frac{1728 x^{5}}{125} - \frac{3159 x^{4}}{500} - \frac{7841 x^{3}}{625} + \frac{121 \log{\left (5 x + 3 \right )}}{78125} + \int \frac{83293}{15625}\, dx + \frac{5569 \int x\, dx}{3125} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**4/(3+5*x),x)

[Out]

54*x**6/5 + 1728*x**5/125 - 3159*x**4/500 - 7841*x**3/625 + 121*log(5*x + 3)/781
25 + Integral(83293/15625, x) + 5569*Integral(x, x)/3125

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Mathematica [A]  time = 0.0195017, size = 42, normalized size = 0.82 \[ \frac{16875000 x^6+21600000 x^5-9871875 x^4-19602500 x^3+1392250 x^2+8329300 x+2420 \log (5 x+3)+2433921}{1562500} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^2*(2 + 3*x)^4)/(3 + 5*x),x]

[Out]

(2433921 + 8329300*x + 1392250*x^2 - 19602500*x^3 - 9871875*x^4 + 21600000*x^5 +
16875000*x^6 + 2420*Log[3 + 5*x])/1562500

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Maple [A]  time = 0.004, size = 38, normalized size = 0.8 \[{\frac{83293\,x}{15625}}+{\frac{5569\,{x}^{2}}{6250}}-{\frac{7841\,{x}^{3}}{625}}-{\frac{3159\,{x}^{4}}{500}}+{\frac{1728\,{x}^{5}}{125}}+{\frac{54\,{x}^{6}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{78125}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^4/(3+5*x),x)

[Out]

83293/15625*x+5569/6250*x^2-7841/625*x^3-3159/500*x^4+1728/125*x^5+54/5*x^6+121/
78125*ln(3+5*x)

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Maxima [A]  time = 1.34143, size = 50, normalized size = 0.98 \[ \frac{54}{5} \, x^{6} + \frac{1728}{125} \, x^{5} - \frac{3159}{500} \, x^{4} - \frac{7841}{625} \, x^{3} + \frac{5569}{6250} \, x^{2} + \frac{83293}{15625} \, x + \frac{121}{78125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^4*(2*x - 1)^2/(5*x + 3),x, algorithm="maxima")

[Out]

54/5*x^6 + 1728/125*x^5 - 3159/500*x^4 - 7841/625*x^3 + 5569/6250*x^2 + 83293/15
625*x + 121/78125*log(5*x + 3)

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Fricas [A]  time = 0.212106, size = 50, normalized size = 0.98 \[ \frac{54}{5} \, x^{6} + \frac{1728}{125} \, x^{5} - \frac{3159}{500} \, x^{4} - \frac{7841}{625} \, x^{3} + \frac{5569}{6250} \, x^{2} + \frac{83293}{15625} \, x + \frac{121}{78125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^4*(2*x - 1)^2/(5*x + 3),x, algorithm="fricas")

[Out]

54/5*x^6 + 1728/125*x^5 - 3159/500*x^4 - 7841/625*x^3 + 5569/6250*x^2 + 83293/15
625*x + 121/78125*log(5*x + 3)

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Sympy [A]  time = 0.184655, size = 48, normalized size = 0.94 \[ \frac{54 x^{6}}{5} + \frac{1728 x^{5}}{125} - \frac{3159 x^{4}}{500} - \frac{7841 x^{3}}{625} + \frac{5569 x^{2}}{6250} + \frac{83293 x}{15625} + \frac{121 \log{\left (5 x + 3 \right )}}{78125} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**4/(3+5*x),x)

[Out]

54*x**6/5 + 1728*x**5/125 - 3159*x**4/500 - 7841*x**3/625 + 5569*x**2/6250 + 832
93*x/15625 + 121*log(5*x + 3)/78125

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GIAC/XCAS [A]  time = 0.209535, size = 51, normalized size = 1. \[ \frac{54}{5} \, x^{6} + \frac{1728}{125} \, x^{5} - \frac{3159}{500} \, x^{4} - \frac{7841}{625} \, x^{3} + \frac{5569}{6250} \, x^{2} + \frac{83293}{15625} \, x + \frac{121}{78125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^4*(2*x - 1)^2/(5*x + 3),x, algorithm="giac")

[Out]

54/5*x^6 + 1728/125*x^5 - 3159/500*x^4 - 7841/625*x^3 + 5569/6250*x^2 + 83293/15
625*x + 121/78125*ln(abs(5*x + 3))