3.1206 \(\int \frac{(1-2 x) (2+3 x)^6}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=66 \[ -\frac{1458 x^5}{625}-\frac{12393 x^4}{2500}-\frac{6399 x^3}{3125}+\frac{297 x^2}{125}+\frac{36936 x}{15625}-\frac{196}{390625 (5 x+3)}-\frac{11}{781250 (5 x+3)^2}+\frac{1449 \log (5 x+3)}{390625} \]

[Out]

(36936*x)/15625 + (297*x^2)/125 - (6399*x^3)/3125 - (12393*x^4)/2500 - (1458*x^5
)/625 - 11/(781250*(3 + 5*x)^2) - 196/(390625*(3 + 5*x)) + (1449*Log[3 + 5*x])/3
90625

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Rubi [A]  time = 0.0756913, antiderivative size = 66, 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 \[ -\frac{1458 x^5}{625}-\frac{12393 x^4}{2500}-\frac{6399 x^3}{3125}+\frac{297 x^2}{125}+\frac{36936 x}{15625}-\frac{196}{390625 (5 x+3)}-\frac{11}{781250 (5 x+3)^2}+\frac{1449 \log (5 x+3)}{390625} \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x)^3,x]

[Out]

(36936*x)/15625 + (297*x^2)/125 - (6399*x^3)/3125 - (12393*x^4)/2500 - (1458*x^5
)/625 - 11/(781250*(3 + 5*x)^2) - 196/(390625*(3 + 5*x)) + (1449*Log[3 + 5*x])/3
90625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{1458 x^{5}}{625} - \frac{12393 x^{4}}{2500} - \frac{6399 x^{3}}{3125} + \frac{1449 \log{\left (5 x + 3 \right )}}{390625} + \int \frac{36936}{15625}\, dx + \frac{594 \int x\, dx}{125} - \frac{196}{390625 \left (5 x + 3\right )} - \frac{11}{781250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(2+3*x)**6/(3+5*x)**3,x)

[Out]

-1458*x**5/625 - 12393*x**4/2500 - 6399*x**3/3125 + 1449*log(5*x + 3)/390625 + I
ntegral(36936/15625, x) + 594*Integral(x, x)/125 - 196/(390625*(5*x + 3)) - 11/(
781250*(5*x + 3)**2)

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Mathematica [A]  time = 0.0330126, size = 61, normalized size = 0.92 \[ \frac{-455625000 x^7-1514953125 x^6-1725806250 x^5-364415625 x^4+874597500 x^3+834723225 x^2+302537270 x+28980 (5 x+3)^2 \log (5 x+3)[phone]}{7812500 (5 x+3)^2} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)*(2 + 3*x)^6)/(3 + 5*x)^3,x]

[Out]

(40891591 + 302537270*x + 834723225*x^2 + 874597500*x^3 - 364415625*x^4 - 172580
6250*x^5 - 1514953125*x^6 - 455625000*x^7 + 28980*(3 + 5*x)^2*Log[3 + 5*x])/(781
2500*(3 + 5*x)^2)

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Maple [A]  time = 0.01, size = 51, normalized size = 0.8 \[{\frac{36936\,x}{15625}}+{\frac{297\,{x}^{2}}{125}}-{\frac{6399\,{x}^{3}}{3125}}-{\frac{12393\,{x}^{4}}{2500}}-{\frac{1458\,{x}^{5}}{625}}-{\frac{11}{781250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{196}{1171875+1953125\,x}}+{\frac{1449\,\ln \left ( 3+5\,x \right ) }{390625}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)^6/(3+5*x)^3,x)

[Out]

36936/15625*x+297/125*x^2-6399/3125*x^3-12393/2500*x^4-1458/625*x^5-11/781250/(3
+5*x)^2-196/390625/(3+5*x)+1449/390625*ln(3+5*x)

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Maxima [A]  time = 1.34556, size = 69, normalized size = 1.05 \[ -\frac{1458}{625} \, x^{5} - \frac{12393}{2500} \, x^{4} - \frac{6399}{3125} \, x^{3} + \frac{297}{125} \, x^{2} + \frac{36936}{15625} \, x - \frac{1960 \, x + 1187}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{1449}{390625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^6*(2*x - 1)/(5*x + 3)^3,x, algorithm="maxima")

[Out]

-1458/625*x^5 - 12393/2500*x^4 - 6399/3125*x^3 + 297/125*x^2 + 36936/15625*x - 1
/781250*(1960*x + 1187)/(25*x^2 + 30*x + 9) + 1449/390625*log(5*x + 3)

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Fricas [A]  time = 0.232456, size = 90, normalized size = 1.36 \[ -\frac{91125000 \, x^{7} + 302990625 \, x^{6} + 345161250 \, x^{5} + 72883125 \, x^{4} - 174919500 \, x^{3} - 144220500 \, x^{2} - 5796 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 33238480 \, x + 2374}{1562500 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^6*(2*x - 1)/(5*x + 3)^3,x, algorithm="fricas")

[Out]

-1/1562500*(91125000*x^7 + 302990625*x^6 + 345161250*x^5 + 72883125*x^4 - 174919
500*x^3 - 144220500*x^2 - 5796*(25*x^2 + 30*x + 9)*log(5*x + 3) - 33238480*x + 2
374)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.297254, size = 56, normalized size = 0.85 \[ - \frac{1458 x^{5}}{625} - \frac{12393 x^{4}}{2500} - \frac{6399 x^{3}}{3125} + \frac{297 x^{2}}{125} + \frac{36936 x}{15625} - \frac{1960 x + 1187}{19531250 x^{2} + 23437500 x + 7031250} + \frac{1449 \log{\left (5 x + 3 \right )}}{390625} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(2+3*x)**6/(3+5*x)**3,x)

[Out]

-1458*x**5/625 - 12393*x**4/2500 - 6399*x**3/3125 + 297*x**2/125 + 36936*x/15625
- (1960*x + 1187)/(19531250*x**2 + 23437500*x + 7031250) + 1449*log(5*x + 3)/39
0625

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GIAC/XCAS [A]  time = 0.211406, size = 63, normalized size = 0.95 \[ -\frac{1458}{625} \, x^{5} - \frac{12393}{2500} \, x^{4} - \frac{6399}{3125} \, x^{3} + \frac{297}{125} \, x^{2} + \frac{36936}{15625} \, x - \frac{1960 \, x + 1187}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{1449}{390625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^6*(2*x - 1)/(5*x + 3)^3,x, algorithm="giac")

[Out]

-1458/625*x^5 - 12393/2500*x^4 - 6399/3125*x^3 + 297/125*x^2 + 36936/15625*x - 1
/781250*(1960*x + 1187)/(5*x + 3)^2 + 1449/390625*ln(abs(5*x + 3))