3.1404 \(\int \frac{(1-2 x)^3 (2+3 x)^4}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=66 \[ -\frac{648 x^5}{625}+\frac{513 x^4}{625}+\frac{2826 x^3}{3125}-\frac{7617 x^2}{6250}+\frac{4691 x}{15625}-\frac{15246}{390625 (5 x+3)}-\frac{1331}{781250 (5 x+3)^2}+\frac{63294 \log (5 x+3)}{390625} \]

[Out]

(4691*x)/15625 - (7617*x^2)/6250 + (2826*x^3)/3125 + (513*x^4)/625 - (648*x^5)/6
25 - 1331/(781250*(3 + 5*x)^2) - 15246/(390625*(3 + 5*x)) + (63294*Log[3 + 5*x])
/390625

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Rubi [A]  time = 0.0804466, 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 \[ -\frac{648 x^5}{625}+\frac{513 x^4}{625}+\frac{2826 x^3}{3125}-\frac{7617 x^2}{6250}+\frac{4691 x}{15625}-\frac{15246}{390625 (5 x+3)}-\frac{1331}{781250 (5 x+3)^2}+\frac{63294 \log (5 x+3)}{390625} \]

Antiderivative was successfully verified.

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

[Out]

(4691*x)/15625 - (7617*x^2)/6250 + (2826*x^3)/3125 + (513*x^4)/625 - (648*x^5)/6
25 - 1331/(781250*(3 + 5*x)^2) - 15246/(390625*(3 + 5*x)) + (63294*Log[3 + 5*x])
/390625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{648 x^{5}}{625} + \frac{513 x^{4}}{625} + \frac{2826 x^{3}}{3125} + \frac{63294 \log{\left (5 x + 3 \right )}}{390625} + \int \frac{4691}{15625}\, dx - \frac{7617 \int x\, dx}{3125} - \frac{15246}{390625 \left (5 x + 3\right )} - \frac{1331}{781250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-648*x**5/625 + 513*x**4/625 + 2826*x**3/3125 + 63294*log(5*x + 3)/390625 + Inte
gral(4691/15625, x) - 7617*Integral(x, x)/3125 - 15246/(390625*(5*x + 3)) - 1331
/(781250*(5*x + 3)**2)

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Mathematica [A]  time = 0.054782, size = 63, normalized size = 0.95 \[ \frac{-101250000 x^7-41343750 x^6+148050000 x^5+15815625 x^4-81707500 x^3+53587800 x^2+83293560 x+632940 (5 x+3)^2 \log (6 (5 x+3))[phone]}{3906250 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

(21586298 + 83293560*x + 53587800*x^2 - 81707500*x^3 + 15815625*x^4 + 148050000*
x^5 - 41343750*x^6 - 101250000*x^7 + 632940*(3 + 5*x)^2*Log[6*(3 + 5*x)])/(39062
50*(3 + 5*x)^2)

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Maple [A]  time = 0.008, size = 51, normalized size = 0.8 \[{\frac{4691\,x}{15625}}-{\frac{7617\,{x}^{2}}{6250}}+{\frac{2826\,{x}^{3}}{3125}}+{\frac{513\,{x}^{4}}{625}}-{\frac{648\,{x}^{5}}{625}}-{\frac{1331}{781250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{15246}{1171875+1953125\,x}}+{\frac{63294\,\ln \left ( 3+5\,x \right ) }{390625}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

4691/15625*x-7617/6250*x^2+2826/3125*x^3+513/625*x^4-648/625*x^5-1331/781250/(3+
5*x)^2-15246/390625/(3+5*x)+63294/390625*ln(3+5*x)

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Maxima [A]  time = 1.36457, size = 69, normalized size = 1.05 \[ -\frac{648}{625} \, x^{5} + \frac{513}{625} \, x^{4} + \frac{2826}{3125} \, x^{3} - \frac{7617}{6250} \, x^{2} + \frac{4691}{15625} \, x - \frac{121 \,{\left (1260 \, x + 767\right )}}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{63294}{390625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-648/625*x^5 + 513/625*x^4 + 2826/3125*x^3 - 7617/6250*x^2 + 4691/15625*x - 121/
781250*(1260*x + 767)/(25*x^2 + 30*x + 9) + 63294/390625*log(5*x + 3)

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Fricas [A]  time = 0.207412, size = 90, normalized size = 1.36 \[ -\frac{20250000 \, x^{7} + 8268750 \, x^{6} - 29610000 \, x^{5} - 3163125 \, x^{4} + 16341500 \, x^{3} + 1532625 \, x^{2} - 126588 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 1958490 \, x + 92807}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/781250*(20250000*x^7 + 8268750*x^6 - 29610000*x^5 - 3163125*x^4 + 16341500*x^
3 + 1532625*x^2 - 126588*(25*x^2 + 30*x + 9)*log(5*x + 3) - 1958490*x + 92807)/(
25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.302394, size = 56, normalized size = 0.85 \[ - \frac{648 x^{5}}{625} + \frac{513 x^{4}}{625} + \frac{2826 x^{3}}{3125} - \frac{7617 x^{2}}{6250} + \frac{4691 x}{15625} - \frac{152460 x + 92807}{19531250 x^{2} + 23437500 x + 7031250} + \frac{63294 \log{\left (5 x + 3 \right )}}{390625} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-648*x**5/625 + 513*x**4/625 + 2826*x**3/3125 - 7617*x**2/6250 + 4691*x/15625 -
(152460*x + 92807)/(19531250*x**2 + 23437500*x + 7031250) + 63294*log(5*x + 3)/3
90625

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GIAC/XCAS [A]  time = 0.209062, size = 63, normalized size = 0.95 \[ -\frac{648}{625} \, x^{5} + \frac{513}{625} \, x^{4} + \frac{2826}{3125} \, x^{3} - \frac{7617}{6250} \, x^{2} + \frac{4691}{15625} \, x - \frac{121 \,{\left (1260 \, x + 767\right )}}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{63294}{390625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-648/625*x^5 + 513/625*x^4 + 2826/3125*x^3 - 7617/6250*x^2 + 4691/15625*x - 121/
781250*(1260*x + 767)/(5*x + 3)^2 + 63294/390625*ln(abs(5*x + 3))