3.1374 \(\int \frac{(1-2 x)^3 (2+3 x)^3}{3+5 x} \, dx\)

Optimal. Leaf size=51 \[ -\frac{36 x^6}{5}+\frac{108 x^5}{125}+\frac{2313 x^4}{250}-\frac{5003 x^3}{1875}-\frac{26241 x^2}{6250}+\frac{41223 x}{15625}+\frac{1331 \log (5 x+3)}{78125} \]

[Out]

(41223*x)/15625 - (26241*x^2)/6250 - (5003*x^3)/1875 + (2313*x^4)/250 + (108*x^5
)/125 - (36*x^6)/5 + (1331*Log[3 + 5*x])/78125

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Rubi [A]  time = 0.0568837, 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 \[ -\frac{36 x^6}{5}+\frac{108 x^5}{125}+\frac{2313 x^4}{250}-\frac{5003 x^3}{1875}-\frac{26241 x^2}{6250}+\frac{41223 x}{15625}+\frac{1331 \log (5 x+3)}{78125} \]

Antiderivative was successfully verified.

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

[Out]

(41223*x)/15625 - (26241*x^2)/6250 - (5003*x^3)/1875 + (2313*x^4)/250 + (108*x^5
)/125 - (36*x^6)/5 + (1331*Log[3 + 5*x])/78125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{36 x^{6}}{5} + \frac{108 x^{5}}{125} + \frac{2313 x^{4}}{250} - \frac{5003 x^{3}}{1875} + \frac{1331 \log{\left (5 x + 3 \right )}}{78125} + \int \frac{41223}{15625}\, dx - \frac{26241 \int x\, dx}{3125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-36*x**6/5 + 108*x**5/125 + 2313*x**4/250 - 5003*x**3/1875 + 1331*log(5*x + 3)/7
8125 + Integral(41223/15625, x) - 26241*Integral(x, x)/3125

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Mathematica [A]  time = 0.0191532, size = 42, normalized size = 0.82 \[ \frac{-16875000 x^6+2025000 x^5+21684375 x^4-6253750 x^3-9840375 x^2+6183450 x+39930 \log (5 x+3)+4036284}{2343750} \]

Antiderivative was successfully verified.

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

[Out]

(4036284 + 6183450*x - 9840375*x^2 - 6253750*x^3 + 21684375*x^4 + 2025000*x^5 -
16875000*x^6 + 39930*Log[3 + 5*x])/2343750

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Maple [A]  time = 0.004, size = 38, normalized size = 0.8 \[{\frac{41223\,x}{15625}}-{\frac{26241\,{x}^{2}}{6250}}-{\frac{5003\,{x}^{3}}{1875}}+{\frac{2313\,{x}^{4}}{250}}+{\frac{108\,{x}^{5}}{125}}-{\frac{36\,{x}^{6}}{5}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{78125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

41223/15625*x-26241/6250*x^2-5003/1875*x^3+2313/250*x^4+108/125*x^5-36/5*x^6+133
1/78125*ln(3+5*x)

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Maxima [A]  time = 1.3497, size = 50, normalized size = 0.98 \[ -\frac{36}{5} \, x^{6} + \frac{108}{125} \, x^{5} + \frac{2313}{250} \, x^{4} - \frac{5003}{1875} \, x^{3} - \frac{26241}{6250} \, x^{2} + \frac{41223}{15625} \, x + \frac{1331}{78125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-36/5*x^6 + 108/125*x^5 + 2313/250*x^4 - 5003/1875*x^3 - 26241/6250*x^2 + 41223/
15625*x + 1331/78125*log(5*x + 3)

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Fricas [A]  time = 0.219454, size = 50, normalized size = 0.98 \[ -\frac{36}{5} \, x^{6} + \frac{108}{125} \, x^{5} + \frac{2313}{250} \, x^{4} - \frac{5003}{1875} \, x^{3} - \frac{26241}{6250} \, x^{2} + \frac{41223}{15625} \, x + \frac{1331}{78125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-36/5*x^6 + 108/125*x^5 + 2313/250*x^4 - 5003/1875*x^3 - 26241/6250*x^2 + 41223/
15625*x + 1331/78125*log(5*x + 3)

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Sympy [A]  time = 0.187383, size = 48, normalized size = 0.94 \[ - \frac{36 x^{6}}{5} + \frac{108 x^{5}}{125} + \frac{2313 x^{4}}{250} - \frac{5003 x^{3}}{1875} - \frac{26241 x^{2}}{6250} + \frac{41223 x}{15625} + \frac{1331 \log{\left (5 x + 3 \right )}}{78125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-36*x**6/5 + 108*x**5/125 + 2313*x**4/250 - 5003*x**3/1875 - 26241*x**2/6250 + 4
1223*x/15625 + 1331*log(5*x + 3)/78125

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GIAC/XCAS [A]  time = 0.206822, size = 51, normalized size = 1. \[ -\frac{36}{5} \, x^{6} + \frac{108}{125} \, x^{5} + \frac{2313}{250} \, x^{4} - \frac{5003}{1875} \, x^{3} - \frac{26241}{6250} \, x^{2} + \frac{41223}{15625} \, x + \frac{1331}{78125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-36/5*x^6 + 108/125*x^5 + 2313/250*x^4 - 5003/1875*x^3 - 26241/6250*x^2 + 41223/
15625*x + 1331/78125*ln(abs(5*x + 3))