3.1273 \(\int \frac{(1-2 x)^2 (2+3 x)^6}{3+5 x} \, dx\)

Optimal. Leaf size=65 \[ \frac{729 x^8}{10}+\frac{34992 x^7}{175}+\frac{35883 x^6}{250}-\frac{228447 x^5}{3125}-\frac{1677159 x^4}{12500}-\frac{422841 x^3}{15625}+\frac{5555569 x^2}{156250}+\frac{8333293 x}{390625}+\frac{121 \log (5 x+3)}{1953125} \]

[Out]

(8333293*x)/390625 + (5555569*x^2)/156250 - (422841*x^3)/15625 - (1677159*x^4)/1
2500 - (228447*x^5)/3125 + (35883*x^6)/250 + (34992*x^7)/175 + (729*x^8)/10 + (1
21*Log[3 + 5*x])/1953125

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Rubi [A]  time = 0.0665661, antiderivative size = 65, 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 \[ \frac{729 x^8}{10}+\frac{34992 x^7}{175}+\frac{35883 x^6}{250}-\frac{228447 x^5}{3125}-\frac{1677159 x^4}{12500}-\frac{422841 x^3}{15625}+\frac{5555569 x^2}{156250}+\frac{8333293 x}{390625}+\frac{121 \log (5 x+3)}{1953125} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x),x]

[Out]

(8333293*x)/390625 + (5555569*x^2)/156250 - (422841*x^3)/15625 - (1677159*x^4)/1
2500 - (228447*x^5)/3125 + (35883*x^6)/250 + (34992*x^7)/175 + (729*x^8)/10 + (1
21*Log[3 + 5*x])/1953125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{729 x^{8}}{10} + \frac{34992 x^{7}}{175} + \frac{35883 x^{6}}{250} - \frac{228447 x^{5}}{3125} - \frac{1677159 x^{4}}{12500} - \frac{422841 x^{3}}{15625} + \frac{121 \log{\left (5 x + 3 \right )}}{1953125} + \int \frac{8333293}{390625}\, dx + \frac{5555569 \int x\, dx}{78125} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**6/(3+5*x),x)

[Out]

729*x**8/10 + 34992*x**7/175 + 35883*x**6/250 - 228447*x**5/3125 - 1677159*x**4/
12500 - 422841*x**3/15625 + 121*log(5*x + 3)/1953125 + Integral(8333293/390625,
x) + 5555569*Integral(x, x)/78125

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Mathematica [A]  time = 0.0216053, size = 52, normalized size = 0.8 \[ \frac{19933593750 x^8+54675000000 x^7+39247031250 x^6-19989112500 x^5-36687853125 x^4-7399717500 x^3+9722245750 x^2+5833305100 x+16940 \log (5 x+3)[phone]}{273437500} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x),x]

[Out]

(966660747 + 5833305100*x + 9722245750*x^2 - 7399717500*x^3 - 36687853125*x^4 -
19989112500*x^5 + 39247031250*x^6 + 54675000000*x^7 + 19933593750*x^8 + 16940*Lo
g[3 + 5*x])/273437500

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Maple [A]  time = 0.004, size = 48, normalized size = 0.7 \[{\frac{8333293\,x}{390625}}+{\frac{5555569\,{x}^{2}}{156250}}-{\frac{422841\,{x}^{3}}{15625}}-{\frac{1677159\,{x}^{4}}{12500}}-{\frac{228447\,{x}^{5}}{3125}}+{\frac{35883\,{x}^{6}}{250}}+{\frac{34992\,{x}^{7}}{175}}+{\frac{729\,{x}^{8}}{10}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{1953125}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^6/(3+5*x),x)

[Out]

8333293/390625*x+5555569/156250*x^2-422841/15625*x^3-1677159/12500*x^4-228447/31
25*x^5+35883/250*x^6+34992/175*x^7+729/10*x^8+121/1953125*ln(3+5*x)

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Maxima [A]  time = 1.34876, size = 63, normalized size = 0.97 \[ \frac{729}{10} \, x^{8} + \frac{34992}{175} \, x^{7} + \frac{35883}{250} \, x^{6} - \frac{228447}{3125} \, x^{5} - \frac{1677159}{12500} \, x^{4} - \frac{422841}{15625} \, x^{3} + \frac{5555569}{156250} \, x^{2} + \frac{8333293}{390625} \, x + \frac{121}{1953125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^6*(2*x - 1)^2/(5*x + 3),x, algorithm="maxima")

[Out]

729/10*x^8 + 34992/175*x^7 + 35883/250*x^6 - 228447/3125*x^5 - 1677159/12500*x^4
- 422841/15625*x^3 + 5555569/156250*x^2 + 8333293/390625*x + 121/1953125*log(5*
x + 3)

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Fricas [A]  time = 0.221291, size = 63, normalized size = 0.97 \[ \frac{729}{10} \, x^{8} + \frac{34992}{175} \, x^{7} + \frac{35883}{250} \, x^{6} - \frac{228447}{3125} \, x^{5} - \frac{1677159}{12500} \, x^{4} - \frac{422841}{15625} \, x^{3} + \frac{5555569}{156250} \, x^{2} + \frac{8333293}{390625} \, x + \frac{121}{1953125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^6*(2*x - 1)^2/(5*x + 3),x, algorithm="fricas")

[Out]

729/10*x^8 + 34992/175*x^7 + 35883/250*x^6 - 228447/3125*x^5 - 1677159/12500*x^4
- 422841/15625*x^3 + 5555569/156250*x^2 + 8333293/390625*x + 121/1953125*log(5*
x + 3)

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Sympy [A]  time = 0.20155, size = 61, normalized size = 0.94 \[ \frac{729 x^{8}}{10} + \frac{34992 x^{7}}{175} + \frac{35883 x^{6}}{250} - \frac{228447 x^{5}}{3125} - \frac{1677159 x^{4}}{12500} - \frac{422841 x^{3}}{15625} + \frac{5555569 x^{2}}{156250} + \frac{8333293 x}{390625} + \frac{121 \log{\left (5 x + 3 \right )}}{1953125} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**6/(3+5*x),x)

[Out]

729*x**8/10 + 34992*x**7/175 + 35883*x**6/250 - 228447*x**5/3125 - 1677159*x**4/
12500 - 422841*x**3/15625 + 5555569*x**2/156250 + 8333293*x/390625 + 121*log(5*x
+ 3)/1953125

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GIAC/XCAS [A]  time = 0.225198, size = 65, normalized size = 1. \[ \frac{729}{10} \, x^{8} + \frac{34992}{175} \, x^{7} + \frac{35883}{250} \, x^{6} - \frac{228447}{3125} \, x^{5} - \frac{1677159}{12500} \, x^{4} - \frac{422841}{15625} \, x^{3} + \frac{5555569}{156250} \, x^{2} + \frac{8333293}{390625} \, x + \frac{121}{1953125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x + 2)^6*(2*x - 1)^2/(5*x + 3),x, algorithm="giac")

[Out]

729/10*x^8 + 34992/175*x^7 + 35883/250*x^6 - 228447/3125*x^5 - 1677159/12500*x^4
- 422841/15625*x^3 + 5555569/156250*x^2 + 8333293/390625*x + 121/1953125*ln(abs
(5*x + 3))