3.1190 \(\int \frac{(1-2 x) (2+3 x)^7}{(3+5 x)^2} \, dx\)

Optimal. Leaf size=69 \[ -\frac{4374 x^7}{175}-\frac{21627 x^6}{250}-\frac{336798 x^5}{3125}-\frac{513783 x^4}{12500}+\frac{92592 x^3}{3125}+\frac{5740767 x^2}{156250}+\frac{5555478 x}{390625}-\frac{11}{1953125 (5 x+3)}+\frac{229 \log (5 x+3)}{1953125} \]

[Out]

(5555478*x)/390625 + (5740767*x^2)/156250 + (92592*x^3)/3125 - (513783*x^4)/1250
0 - (336798*x^5)/3125 - (21627*x^6)/250 - (4374*x^7)/175 - 11/(1953125*(3 + 5*x)
) + (229*Log[3 + 5*x])/1953125

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Rubi [A]  time = 0.0783194, antiderivative size = 69, 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 \[ -\frac{4374 x^7}{175}-\frac{21627 x^6}{250}-\frac{336798 x^5}{3125}-\frac{513783 x^4}{12500}+\frac{92592 x^3}{3125}+\frac{5740767 x^2}{156250}+\frac{5555478 x}{390625}-\frac{11}{1953125 (5 x+3)}+\frac{229 \log (5 x+3)}{1953125} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)*(2 + 3*x)^7)/(3 + 5*x)^2,x]

[Out]

(5555478*x)/390625 + (5740767*x^2)/156250 + (92592*x^3)/3125 - (513783*x^4)/1250
0 - (336798*x^5)/3125 - (21627*x^6)/250 - (4374*x^7)/175 - 11/(1953125*(3 + 5*x)
) + (229*Log[3 + 5*x])/1953125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{4374 x^{7}}{175} - \frac{21627 x^{6}}{250} - \frac{336798 x^{5}}{3125} - \frac{513783 x^{4}}{12500} + \frac{92592 x^{3}}{3125} + \frac{229 \log{\left (5 x + 3 \right )}}{1953125} + \int \frac{5555478}{390625}\, dx + \frac{5740767 \int x\, dx}{78125} - \frac{11}{1953125 \left (5 x + 3\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(2+3*x)**7/(3+5*x)**2,x)

[Out]

-4374*x**7/175 - 21627*x**6/250 - 336798*x**5/3125 - 513783*x**4/12500 + 92592*x
**3/3125 + 229*log(5*x + 3)/1953125 + Integral(5555478/390625, x) + 5740767*Inte
gral(x, x)/78125 - 11/(1953125*(5*x + 3))

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Mathematica [A]  time = 0.0597866, size = 85, normalized size = 1.23 \[ \frac{-1875000 (3 x+2)^7+6781250 (3 x+2)^6+3360000 (3 x+2)^5+1273125 (3 x+2)^4+455000 (3 x+2)^3+171150 (3 x+2)^2+82320 (3 x+2)-\frac{924}{5 x+3}+19236 \log (-3 (5 x+3))}{164062500} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)*(2 + 3*x)^7)/(3 + 5*x)^2,x]

[Out]

(82320*(2 + 3*x) + 171150*(2 + 3*x)^2 + 455000*(2 + 3*x)^3 + 1273125*(2 + 3*x)^4
+ 3360000*(2 + 3*x)^5 + 6781250*(2 + 3*x)^6 - 1875000*(2 + 3*x)^7 - 924/(3 + 5*
x) + 19236*Log[-3*(3 + 5*x)])/164062500

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Maple [A]  time = 0.01, size = 52, normalized size = 0.8 \[{\frac{5555478\,x}{390625}}+{\frac{5740767\,{x}^{2}}{156250}}+{\frac{92592\,{x}^{3}}{3125}}-{\frac{513783\,{x}^{4}}{12500}}-{\frac{336798\,{x}^{5}}{3125}}-{\frac{21627\,{x}^{6}}{250}}-{\frac{4374\,{x}^{7}}{175}}-{\frac{11}{5859375+9765625\,x}}+{\frac{229\,\ln \left ( 3+5\,x \right ) }{1953125}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)^7/(3+5*x)^2,x)

[Out]

5555478/390625*x+5740767/156250*x^2+92592/3125*x^3-513783/12500*x^4-336798/3125*
x^5-21627/250*x^6-4374/175*x^7-11/1953125/(3+5*x)+229/1953125*ln(3+5*x)

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Maxima [A]  time = 1.3388, size = 69, normalized size = 1. \[ -\frac{4374}{175} \, x^{7} - \frac{21627}{250} \, x^{6} - \frac{336798}{3125} \, x^{5} - \frac{513783}{12500} \, x^{4} + \frac{92592}{3125} \, x^{3} + \frac{5740767}{156250} \, x^{2} + \frac{5555478}{390625} \, x - \frac{11}{1953125 \,{\left (5 \, x + 3\right )}} + \frac{229}{1953125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^7*(2*x - 1)/(5*x + 3)^2,x, algorithm="maxima")

[Out]

-4374/175*x^7 - 21627/250*x^6 - 336798/3125*x^5 - 513783/12500*x^4 + 92592/3125*
x^3 + 5740767/156250*x^2 + 5555478/390625*x - 11/1953125/(5*x + 3) + 229/1953125
*log(5*x + 3)

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Fricas [A]  time = 0.210104, size = 84, normalized size = 1.22 \[ -\frac{6834375000 \, x^{8} + 27755156250 \, x^{7} + 43662543750 \, x^{6} + 28920898125 \, x^{5} - 1358398125 \, x^{4} - 14907422250 \, x^{3} - 9916639950 \, x^{2} - 6412 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 2333300760 \, x + 308}{54687500 \,{\left (5 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^7*(2*x - 1)/(5*x + 3)^2,x, algorithm="fricas")

[Out]

-1/54687500*(6834375000*x^8 + 27755156250*x^7 + 43662543750*x^6 + 28920898125*x^
5 - 1358398125*x^4 - 14907422250*x^3 - 9916639950*x^2 - 6412*(5*x + 3)*log(5*x +
3) - 2333300760*x + 308)/(5*x + 3)

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Sympy [A]  time = 0.245303, size = 61, normalized size = 0.88 \[ - \frac{4374 x^{7}}{175} - \frac{21627 x^{6}}{250} - \frac{336798 x^{5}}{3125} - \frac{513783 x^{4}}{12500} + \frac{92592 x^{3}}{3125} + \frac{5740767 x^{2}}{156250} + \frac{5555478 x}{390625} + \frac{229 \log{\left (5 x + 3 \right )}}{1953125} - \frac{11}{9765625 x + 5859375} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(2+3*x)**7/(3+5*x)**2,x)

[Out]

-4374*x**7/175 - 21627*x**6/250 - 336798*x**5/3125 - 513783*x**4/12500 + 92592*x
**3/3125 + 5740767*x**2/156250 + 5555478*x/390625 + 229*log(5*x + 3)/1953125 - 1
1/(9765625*x + 5859375)

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GIAC/XCAS [A]  time = 0.21031, size = 126, normalized size = 1.83 \[ \frac{3}{273437500} \,{\left (5 \, x + 3\right )}^{7}{\left (\frac{107730}{5 \, x + 3} + \frac{428652}{{\left (5 \, x + 3\right )}^{2}} + \frac{588735}{{\left (5 \, x + 3\right )}^{3}} + \frac{455700}{{\left (5 \, x + 3\right )}^{4}} + \frac{233730}{{\left (5 \, x + 3\right )}^{5}} + \frac{95060}{{\left (5 \, x + 3\right )}^{6}} - 29160\right )} - \frac{11}{1953125 \,{\left (5 \, x + 3\right )}} - \frac{229}{1953125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^7*(2*x - 1)/(5*x + 3)^2,x, algorithm="giac")

[Out]

3/273437500*(5*x + 3)^7*(107730/(5*x + 3) + 428652/(5*x + 3)^2 + 588735/(5*x + 3
)^3 + 455700/(5*x + 3)^4 + 233730/(5*x + 3)^5 + 95060/(5*x + 3)^6 - 29160) - 11/
1953125/(5*x + 3) - 229/1953125*ln(1/5*abs(5*x + 3)/(5*x + 3)^2)