3.1208 \(\int \frac{(1-2 x) (2+3 x)^4}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=52 \[ -\frac{54 x^3}{125}-\frac{297 x^2}{1250}+\frac{1647 x}{3125}-\frac{26}{3125 (5 x+3)}-\frac{11}{31250 (5 x+3)^2}+\frac{114 \log (5 x+3)}{3125} \]

[Out]

(1647*x)/3125 - (297*x^2)/1250 - (54*x^3)/125 - 11/(31250*(3 + 5*x)^2) - 26/(312
5*(3 + 5*x)) + (114*Log[3 + 5*x])/3125

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Rubi [A]  time = 0.0615155, antiderivative size = 52, 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 \[ -\frac{54 x^3}{125}-\frac{297 x^2}{1250}+\frac{1647 x}{3125}-\frac{26}{3125 (5 x+3)}-\frac{11}{31250 (5 x+3)^2}+\frac{114 \log (5 x+3)}{3125} \]

Antiderivative was successfully verified.

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

[Out]

(1647*x)/3125 - (297*x^2)/1250 - (54*x^3)/125 - 11/(31250*(3 + 5*x)^2) - 26/(312
5*(3 + 5*x)) + (114*Log[3 + 5*x])/3125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{54 x^{3}}{125} + \frac{114 \log{\left (5 x + 3 \right )}}{3125} + \int \frac{1647}{3125}\, dx - \frac{297 \int x\, dx}{625} - \frac{26}{3125 \left (5 x + 3\right )} - \frac{11}{31250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-54*x**3/125 + 114*log(5*x + 3)/3125 + Integral(1647/3125, x) - 297*Integral(x,
x)/625 - 26/(3125*(5*x + 3)) - 11/(31250*(5*x + 3)**2)

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Mathematica [A]  time = 0.0293316, size = 51, normalized size = 0.98 \[ \frac{-67500 x^5-118125 x^4+13500 x^3+133650 x^2+87220 x+228 (5 x+3)^2 \log (5 x+3)+17192}{6250 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

(17192 + 87220*x + 133650*x^2 + 13500*x^3 - 118125*x^4 - 67500*x^5 + 228*(3 + 5*
x)^2*Log[3 + 5*x])/(6250*(3 + 5*x)^2)

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Maple [A]  time = 0.01, size = 41, normalized size = 0.8 \[{\frac{1647\,x}{3125}}-{\frac{297\,{x}^{2}}{1250}}-{\frac{54\,{x}^{3}}{125}}-{\frac{11}{31250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{26}{9375+15625\,x}}+{\frac{114\,\ln \left ( 3+5\,x \right ) }{3125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1647/3125*x-297/1250*x^2-54/125*x^3-11/31250/(3+5*x)^2-26/3125/(3+5*x)+114/3125*
ln(3+5*x)

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Maxima [A]  time = 1.35377, size = 55, normalized size = 1.06 \[ -\frac{54}{125} \, x^{3} - \frac{297}{1250} \, x^{2} + \frac{1647}{3125} \, x - \frac{1300 \, x + 791}{31250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{114}{3125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-54/125*x^3 - 297/1250*x^2 + 1647/3125*x - 1/31250*(1300*x + 791)/(25*x^2 + 30*x
+ 9) + 114/3125*log(5*x + 3)

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Fricas [A]  time = 0.2341, size = 77, normalized size = 1.48 \[ -\frac{337500 \, x^{5} + 590625 \, x^{4} - 67500 \, x^{3} - 427275 \, x^{2} - 1140 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 146930 \, x + 791}{31250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/31250*(337500*x^5 + 590625*x^4 - 67500*x^3 - 427275*x^2 - 1140*(25*x^2 + 30*x
+ 9)*log(5*x + 3) - 146930*x + 791)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.277824, size = 42, normalized size = 0.81 \[ - \frac{54 x^{3}}{125} - \frac{297 x^{2}}{1250} + \frac{1647 x}{3125} - \frac{1300 x + 791}{781250 x^{2} + 937500 x + 281250} + \frac{114 \log{\left (5 x + 3 \right )}}{3125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-54*x**3/125 - 297*x**2/1250 + 1647*x/3125 - (1300*x + 791)/(781250*x**2 + 93750
0*x + 281250) + 114*log(5*x + 3)/3125

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GIAC/XCAS [A]  time = 0.211187, size = 50, normalized size = 0.96 \[ -\frac{54}{125} \, x^{3} - \frac{297}{1250} \, x^{2} + \frac{1647}{3125} \, x - \frac{1300 \, x + 791}{31250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{114}{3125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-54/125*x^3 - 297/1250*x^2 + 1647/3125*x - 1/31250*(1300*x + 791)/(5*x + 3)^2 +
114/3125*ln(abs(5*x + 3))