3.1307 \(\int \frac{(1-2 x)^2 (2+3 x)^5}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=66 \[ \frac{972 x^5}{625}+\frac{648 x^4}{625}-\frac{5499 x^3}{3125}-\frac{5301 x^2}{6250}+\frac{17796 x}{15625}-\frac{1771}{390625 (5 x+3)}-\frac{121}{781250 (5 x+3)^2}+\frac{10234 \log (5 x+3)}{390625} \]

[Out]

(17796*x)/15625 - (5301*x^2)/6250 - (5499*x^3)/3125 + (648*x^4)/625 + (972*x^5)/
625 - 121/(781250*(3 + 5*x)^2) - 1771/(390625*(3 + 5*x)) + (10234*Log[3 + 5*x])/
390625

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Rubi [A]  time = 0.0827338, antiderivative size = 66, 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 \[ \frac{972 x^5}{625}+\frac{648 x^4}{625}-\frac{5499 x^3}{3125}-\frac{5301 x^2}{6250}+\frac{17796 x}{15625}-\frac{1771}{390625 (5 x+3)}-\frac{121}{781250 (5 x+3)^2}+\frac{10234 \log (5 x+3)}{390625} \]

Antiderivative was successfully verified.

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

[Out]

(17796*x)/15625 - (5301*x^2)/6250 - (5499*x^3)/3125 + (648*x^4)/625 + (972*x^5)/
625 - 121/(781250*(3 + 5*x)^2) - 1771/(390625*(3 + 5*x)) + (10234*Log[3 + 5*x])/
390625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{972 x^{5}}{625} + \frac{648 x^{4}}{625} - \frac{5499 x^{3}}{3125} + \frac{10234 \log{\left (5 x + 3 \right )}}{390625} + \int \frac{17796}{15625}\, dx - \frac{5301 \int x\, dx}{3125} - \frac{1771}{390625 \left (5 x + 3\right )} - \frac{121}{781250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

972*x**5/625 + 648*x**4/625 - 5499*x**3/3125 + 10234*log(5*x + 3)/390625 + Integ
ral(17796/15625, x) - 5301*Integral(x, x)/3125 - 1771/(390625*(5*x + 3)) - 121/(
781250*(5*x + 3)**2)

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Mathematica [A]  time = 0.0557577, size = 63, normalized size = 0.95 \[ \frac{151875000 x^7+283500000 x^6+4331250 x^5-252590625 x^4-50032500 x^3+161774550 x^2+109699660 x+102340 (5 x+3)^2 \log (6 (5 x+3))[phone]}{3906250 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

(20870428 + 109699660*x + 161774550*x^2 - 50032500*x^3 - 252590625*x^4 + 4331250
*x^5 + 283500000*x^6 + 151875000*x^7 + 102340*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(390
6250*(3 + 5*x)^2)

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Maple [A]  time = 0.011, size = 51, normalized size = 0.8 \[{\frac{17796\,x}{15625}}-{\frac{5301\,{x}^{2}}{6250}}-{\frac{5499\,{x}^{3}}{3125}}+{\frac{648\,{x}^{4}}{625}}+{\frac{972\,{x}^{5}}{625}}-{\frac{121}{781250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{1771}{1171875+1953125\,x}}+{\frac{10234\,\ln \left ( 3+5\,x \right ) }{390625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

17796/15625*x-5301/6250*x^2-5499/3125*x^3+648/625*x^4+972/625*x^5-121/781250/(3+
5*x)^2-1771/390625/(3+5*x)+10234/390625*ln(3+5*x)

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Maxima [A]  time = 1.32221, size = 69, normalized size = 1.05 \[ \frac{972}{625} \, x^{5} + \frac{648}{625} \, x^{4} - \frac{5499}{3125} \, x^{3} - \frac{5301}{6250} \, x^{2} + \frac{17796}{15625} \, x - \frac{11 \,{\left (1610 \, x + 977\right )}}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{10234}{390625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

972/625*x^5 + 648/625*x^4 - 5499/3125*x^3 - 5301/6250*x^2 + 17796/15625*x - 11/7
81250*(1610*x + 977)/(25*x^2 + 30*x + 9) + 10234/390625*log(5*x + 3)

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Fricas [A]  time = 0.205595, size = 90, normalized size = 1.36 \[ \frac{30375000 \, x^{7} + 56700000 \, x^{6} + 866250 \, x^{5} - 50518125 \, x^{4} - 10006500 \, x^{3} + 20730375 \, x^{2} + 20468 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 7990490 \, x - 10747}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/781250*(30375000*x^7 + 56700000*x^6 + 866250*x^5 - 50518125*x^4 - 10006500*x^3
+ 20730375*x^2 + 20468*(25*x^2 + 30*x + 9)*log(5*x + 3) + 7990490*x - 10747)/(2
5*x^2 + 30*x + 9)

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Sympy [A]  time = 0.309937, size = 56, normalized size = 0.85 \[ \frac{972 x^{5}}{625} + \frac{648 x^{4}}{625} - \frac{5499 x^{3}}{3125} - \frac{5301 x^{2}}{6250} + \frac{17796 x}{15625} - \frac{17710 x + 10747}{19531250 x^{2} + 23437500 x + 7031250} + \frac{10234 \log{\left (5 x + 3 \right )}}{390625} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

972*x**5/625 + 648*x**4/625 - 5499*x**3/3125 - 5301*x**2/6250 + 17796*x/15625 -
(17710*x + 10747)/(19531250*x**2 + 23437500*x + 7031250) + 10234*log(5*x + 3)/39
0625

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GIAC/XCAS [A]  time = 0.206552, size = 63, normalized size = 0.95 \[ \frac{972}{625} \, x^{5} + \frac{648}{625} \, x^{4} - \frac{5499}{3125} \, x^{3} - \frac{5301}{6250} \, x^{2} + \frac{17796}{15625} \, x - \frac{11 \,{\left (1610 \, x + 977\right )}}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{10234}{390625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

972/625*x^5 + 648/625*x^4 - 5499/3125*x^3 - 5301/6250*x^2 + 17796/15625*x - 11/7
81250*(1610*x + 977)/(5*x + 3)^2 + 10234/390625*ln(abs(5*x + 3))