3.1192 \(\int \frac{(1-2 x) (2+3 x)^5}{(3+5 x)^2} \, dx\)

Optimal. Leaf size=55 \[ -\frac{486 x^5}{125}-\frac{3969 x^4}{500}-\frac{1854 x^3}{625}+\frac{24093 x^2}{6250}+\frac{444 x}{125}-\frac{11}{78125 (5 x+3)}+\frac{163 \log (5 x+3)}{78125} \]

[Out]

(444*x)/125 + (24093*x^2)/6250 - (1854*x^3)/625 - (3969*x^4)/500 - (486*x^5)/125
- 11/(78125*(3 + 5*x)) + (163*Log[3 + 5*x])/78125

_______________________________________________________________________________________

Rubi [A]  time = 0.0636453, antiderivative size = 55, 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 \[ -\frac{486 x^5}{125}-\frac{3969 x^4}{500}-\frac{1854 x^3}{625}+\frac{24093 x^2}{6250}+\frac{444 x}{125}-\frac{11}{78125 (5 x+3)}+\frac{163 \log (5 x+3)}{78125} \]

Antiderivative was successfully verified.

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

[Out]

(444*x)/125 + (24093*x^2)/6250 - (1854*x^3)/625 - (3969*x^4)/500 - (486*x^5)/125
- 11/(78125*(3 + 5*x)) + (163*Log[3 + 5*x])/78125

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{486 x^{5}}{125} - \frac{3969 x^{4}}{500} - \frac{1854 x^{3}}{625} + \frac{163 \log{\left (5 x + 3 \right )}}{78125} + \int \frac{444}{125}\, dx + \frac{24093 \int x\, dx}{3125} - \frac{11}{78125 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-486*x**5/125 - 3969*x**4/500 - 1854*x**3/625 + 163*log(5*x + 3)/78125 + Integra
l(444/125, x) + 24093*Integral(x, x)/3125 - 11/(78125*(5*x + 3))

_______________________________________________________________________________________

Mathematica [A]  time = 0.0308553, size = 48, normalized size = 0.87 \[ \frac{-3645000 x^5-7441875 x^4-2781000 x^3+3613950 x^2+3330000 x-\frac{132}{5 x+3}+1956 \log (-3 (5 x+3))+779800}{937500} \]

Antiderivative was successfully verified.

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

[Out]

(779800 + 3330000*x + 3613950*x^2 - 2781000*x^3 - 7441875*x^4 - 3645000*x^5 - 13
2/(3 + 5*x) + 1956*Log[-3*(3 + 5*x)])/937500

_______________________________________________________________________________________

Maple [A]  time = 0.009, size = 42, normalized size = 0.8 \[{\frac{444\,x}{125}}+{\frac{24093\,{x}^{2}}{6250}}-{\frac{1854\,{x}^{3}}{625}}-{\frac{3969\,{x}^{4}}{500}}-{\frac{486\,{x}^{5}}{125}}-{\frac{11}{234375+390625\,x}}+{\frac{163\,\ln \left ( 3+5\,x \right ) }{78125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

444/125*x+24093/6250*x^2-1854/625*x^3-3969/500*x^4-486/125*x^5-11/78125/(3+5*x)+
163/78125*ln(3+5*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34593, size = 55, normalized size = 1. \[ -\frac{486}{125} \, x^{5} - \frac{3969}{500} \, x^{4} - \frac{1854}{625} \, x^{3} + \frac{24093}{6250} \, x^{2} + \frac{444}{125} \, x - \frac{11}{78125 \,{\left (5 \, x + 3\right )}} + \frac{163}{78125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-486/125*x^5 - 3969/500*x^4 - 1854/625*x^3 + 24093/6250*x^2 + 444/125*x - 11/781
25/(5*x + 3) + 163/78125*log(5*x + 3)

_______________________________________________________________________________________

Fricas [A]  time = 0.207363, size = 70, normalized size = 1.27 \[ -\frac{6075000 \, x^{6} + 16048125 \, x^{5} + 12076875 \, x^{4} - 3242250 \, x^{3} - 9163950 \, x^{2} - 652 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 3330000 \, x + 44}{312500 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/312500*(6075000*x^6 + 16048125*x^5 + 12076875*x^4 - 3242250*x^3 - 9163950*x^2
- 652*(5*x + 3)*log(5*x + 3) - 3330000*x + 44)/(5*x + 3)

_______________________________________________________________________________________

Sympy [A]  time = 0.23521, size = 48, normalized size = 0.87 \[ - \frac{486 x^{5}}{125} - \frac{3969 x^{4}}{500} - \frac{1854 x^{3}}{625} + \frac{24093 x^{2}}{6250} + \frac{444 x}{125} + \frac{163 \log{\left (5 x + 3 \right )}}{78125} - \frac{11}{390625 x + 234375} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-486*x**5/125 - 3969*x**4/500 - 1854*x**3/625 + 24093*x**2/6250 + 444*x/125 + 16
3*log(5*x + 3)/78125 - 11/(390625*x + 234375)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.210981, size = 101, normalized size = 1.84 \[ \frac{3}{1562500} \,{\left (5 \, x + 3\right )}^{5}{\left (\frac{3105}{5 \, x + 3} + \frac{8700}{{\left (5 \, x + 3\right )}^{2}} + \frac{9300}{{\left (5 \, x + 3\right )}^{3}} + \frac{6400}{{\left (5 \, x + 3\right )}^{4}} - 648\right )} - \frac{11}{78125 \,{\left (5 \, x + 3\right )}} - \frac{163}{78125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/1562500*(5*x + 3)^5*(3105/(5*x + 3) + 8700/(5*x + 3)^2 + 9300/(5*x + 3)^3 + 64
00/(5*x + 3)^4 - 648) - 11/78125/(5*x + 3) - 163/78125*ln(1/5*abs(5*x + 3)/(5*x
+ 3)^2)