3.1207 \(\int \frac{(1-2 x) (2+3 x)^5}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=59 \[ -\frac{243 x^4}{250}-\frac{837 x^3}{625}+\frac{1971 x^2}{6250}+\frac{3636 x}{3125}-\frac{163}{78125 (5 x+3)}-\frac{11}{156250 (5 x+3)^2}+\frac{192 \log (5 x+3)}{15625} \]

[Out]

(3636*x)/3125 + (1971*x^2)/6250 - (837*x^3)/625 - (243*x^4)/250 - 11/(156250*(3
+ 5*x)^2) - 163/(78125*(3 + 5*x)) + (192*Log[3 + 5*x])/15625

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Rubi [A]  time = 0.0708468, antiderivative size = 59, 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 \[ -\frac{243 x^4}{250}-\frac{837 x^3}{625}+\frac{1971 x^2}{6250}+\frac{3636 x}{3125}-\frac{163}{78125 (5 x+3)}-\frac{11}{156250 (5 x+3)^2}+\frac{192 \log (5 x+3)}{15625} \]

Antiderivative was successfully verified.

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

[Out]

(3636*x)/3125 + (1971*x^2)/6250 - (837*x^3)/625 - (243*x^4)/250 - 11/(156250*(3
+ 5*x)^2) - 163/(78125*(3 + 5*x)) + (192*Log[3 + 5*x])/15625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{243 x^{4}}{250} - \frac{837 x^{3}}{625} + \frac{192 \log{\left (5 x + 3 \right )}}{15625} + \int \frac{3636}{3125}\, dx + \frac{1971 \int x\, dx}{3125} - \frac{163}{78125 \left (5 x + 3\right )} - \frac{11}{156250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x**4/250 - 837*x**3/625 + 192*log(5*x + 3)/15625 + Integral(3636/3125, x) +
1971*Integral(x, x)/3125 - 163/(78125*(5*x + 3)) - 11/(156250*(5*x + 3)**2)

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Mathematica [A]  time = 0.026948, size = 58, normalized size = 0.98 \[ \frac{-3796875 x^6-9787500 x^5-6412500 x^4+4140000 x^3+7579975 x^2+3653570 x+1920 (5 x+3)^2 \log (-3 (5 x+3))+604711}{156250 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

(604711 + 3653570*x + 7579975*x^2 + 4140000*x^3 - 6412500*x^4 - 9787500*x^5 - 37
96875*x^6 + 1920*(3 + 5*x)^2*Log[-3*(3 + 5*x)])/(156250*(3 + 5*x)^2)

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Maple [A]  time = 0.01, size = 46, normalized size = 0.8 \[{\frac{3636\,x}{3125}}+{\frac{1971\,{x}^{2}}{6250}}-{\frac{837\,{x}^{3}}{625}}-{\frac{243\,{x}^{4}}{250}}-{\frac{11}{156250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{163}{234375+390625\,x}}+{\frac{192\,\ln \left ( 3+5\,x \right ) }{15625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3636/3125*x+1971/6250*x^2-837/625*x^3-243/250*x^4-11/156250/(3+5*x)^2-163/78125/
(3+5*x)+192/15625*ln(3+5*x)

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Maxima [A]  time = 1.35196, size = 62, normalized size = 1.05 \[ -\frac{243}{250} \, x^{4} - \frac{837}{625} \, x^{3} + \frac{1971}{6250} \, x^{2} + \frac{3636}{3125} \, x - \frac{1630 \, x + 989}{156250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{192}{15625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/250*x^4 - 837/625*x^3 + 1971/6250*x^2 + 3636/3125*x - 1/156250*(1630*x + 98
9)/(25*x^2 + 30*x + 9) + 192/15625*log(5*x + 3)

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Fricas [A]  time = 0.227126, size = 84, normalized size = 1.42 \[ -\frac{3796875 \, x^{6} + 9787500 \, x^{5} + 6412500 \, x^{4} - 4140000 \, x^{3} - 5897475 \, x^{2} - 1920 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 1634570 \, x + 989}{156250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/156250*(3796875*x^6 + 9787500*x^5 + 6412500*x^4 - 4140000*x^3 - 5897475*x^2 -
1920*(25*x^2 + 30*x + 9)*log(5*x + 3) - 1634570*x + 989)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.285152, size = 49, normalized size = 0.83 \[ - \frac{243 x^{4}}{250} - \frac{837 x^{3}}{625} + \frac{1971 x^{2}}{6250} + \frac{3636 x}{3125} - \frac{1630 x + 989}{3906250 x^{2} + 4687500 x + 1406250} + \frac{192 \log{\left (5 x + 3 \right )}}{15625} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x**4/250 - 837*x**3/625 + 1971*x**2/6250 + 3636*x/3125 - (1630*x + 989)/(39
06250*x**2 + 4687500*x + 1406250) + 192*log(5*x + 3)/15625

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GIAC/XCAS [A]  time = 0.206999, size = 57, normalized size = 0.97 \[ -\frac{243}{250} \, x^{4} - \frac{837}{625} \, x^{3} + \frac{1971}{6250} \, x^{2} + \frac{3636}{3125} \, x - \frac{1630 \, x + 989}{156250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{192}{15625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/250*x^4 - 837/625*x^3 + 1971/6250*x^2 + 3636/3125*x - 1/156250*(1630*x + 98
9)/(5*x + 3)^2 + 192/15625*ln(abs(5*x + 3))