3.1403 \(\int \frac{(1-2 x)^3 (2+3 x)^5}{(3+5 x)^3} \, dx\)

Optimal. Leaf size=73 \[ -\frac{324 x^6}{125}-\frac{324 x^5}{3125}+\frac{22977 x^4}{6250}-\frac{393 x^3}{625}-\frac{62097 x^2}{31250}+\frac{424432 x}{390625}-\frac{19239}{1953125 (5 x+3)}-\frac{1331}{3906250 (5 x+3)^2}+\frac{109032 \log (5 x+3)}{1953125} \]

[Out]

(424432*x)/390625 - (62097*x^2)/31250 - (393*x^3)/625 + (22977*x^4)/6250 - (324*
x^5)/3125 - (324*x^6)/125 - 1331/(3906250*(3 + 5*x)^2) - 19239/(1953125*(3 + 5*x
)) + (109032*Log[3 + 5*x])/1953125

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Rubi [A]  time = 0.0902944, antiderivative size = 73, 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 \[ -\frac{324 x^6}{125}-\frac{324 x^5}{3125}+\frac{22977 x^4}{6250}-\frac{393 x^3}{625}-\frac{62097 x^2}{31250}+\frac{424432 x}{390625}-\frac{19239}{1953125 (5 x+3)}-\frac{1331}{3906250 (5 x+3)^2}+\frac{109032 \log (5 x+3)}{1953125} \]

Antiderivative was successfully verified.

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

[Out]

(424432*x)/390625 - (62097*x^2)/31250 - (393*x^3)/625 + (22977*x^4)/6250 - (324*
x^5)/3125 - (324*x^6)/125 - 1331/(3906250*(3 + 5*x)^2) - 19239/(1953125*(3 + 5*x
)) + (109032*Log[3 + 5*x])/1953125

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{324 x^{6}}{125} - \frac{324 x^{5}}{3125} + \frac{22977 x^{4}}{6250} - \frac{393 x^{3}}{625} + \frac{109032 \log{\left (5 x + 3 \right )}}{1953125} + \int \frac{424432}{390625}\, dx - \frac{62097 \int x\, dx}{15625} - \frac{19239}{1953125 \left (5 x + 3\right )} - \frac{1331}{3906250 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-324*x**6/125 - 324*x**5/3125 + 22977*x**4/6250 - 393*x**3/625 + 109032*log(5*x
+ 3)/1953125 + Integral(424432/390625, x) - 62097*Integral(x, x)/15625 - 19239/(
1953125*(5*x + 3)) - 1331/(3906250*(5*x + 3)**2)

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Mathematica [A]  time = 0.0583319, size = 68, normalized size = 0.93 \[ \frac{-1265625000 x^8-1569375000 x^7+1278703125 x^6+1828837500 x^5-692475000 x^4-744310000 x^3+711123525 x^2+698557830 x+1090320 (5 x+3)^2 \log (6 (5 x+3))[phone]}{19531250 (5 x+3)^2} \]

Antiderivative was successfully verified.

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

[Out]

(151973789 + 698557830*x + 711123525*x^2 - 744310000*x^3 - 692475000*x^4 + 18288
37500*x^5 + 1278703125*x^6 - 1569375000*x^7 - 1265625000*x^8 + 1090320*(3 + 5*x)
^2*Log[6*(3 + 5*x)])/(19531250*(3 + 5*x)^2)

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Maple [A]  time = 0.01, size = 56, normalized size = 0.8 \[{\frac{424432\,x}{390625}}-{\frac{62097\,{x}^{2}}{31250}}-{\frac{393\,{x}^{3}}{625}}+{\frac{22977\,{x}^{4}}{6250}}-{\frac{324\,{x}^{5}}{3125}}-{\frac{324\,{x}^{6}}{125}}-{\frac{1331}{3906250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{19239}{5859375+9765625\,x}}+{\frac{109032\,\ln \left ( 3+5\,x \right ) }{1953125}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

424432/390625*x-62097/31250*x^2-393/625*x^3+22977/6250*x^4-324/3125*x^5-324/125*
x^6-1331/3906250/(3+5*x)^2-19239/1953125/(3+5*x)+109032/1953125*ln(3+5*x)

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Maxima [A]  time = 1.3289, size = 76, normalized size = 1.04 \[ -\frac{324}{125} \, x^{6} - \frac{324}{3125} \, x^{5} + \frac{22977}{6250} \, x^{4} - \frac{393}{625} \, x^{3} - \frac{62097}{31250} \, x^{2} + \frac{424432}{390625} \, x - \frac{121 \,{\left (318 \, x + 193\right )}}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{109032}{1953125} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-324/125*x^6 - 324/3125*x^5 + 22977/6250*x^4 - 393/625*x^3 - 62097/31250*x^2 + 4
24432/390625*x - 121/781250*(318*x + 193)/(25*x^2 + 30*x + 9) + 109032/1953125*l
og(5*x + 3)

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Fricas [A]  time = 0.211732, size = 97, normalized size = 1.33 \[ -\frac{253125000 \, x^{8} + 313875000 \, x^{7} - 255740625 \, x^{6} - 365767500 \, x^{5} + 138495000 \, x^{4} + 148862000 \, x^{3} - 57470475 \, x^{2} - 218064 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 38006490 \, x + 116765}{3906250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3906250*(253125000*x^8 + 313875000*x^7 - 255740625*x^6 - 365767500*x^5 + 1384
95000*x^4 + 148862000*x^3 - 57470475*x^2 - 218064*(25*x^2 + 30*x + 9)*log(5*x +
3) - 38006490*x + 116765)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.313781, size = 63, normalized size = 0.86 \[ - \frac{324 x^{6}}{125} - \frac{324 x^{5}}{3125} + \frac{22977 x^{4}}{6250} - \frac{393 x^{3}}{625} - \frac{62097 x^{2}}{31250} + \frac{424432 x}{390625} - \frac{38478 x + 23353}{19531250 x^{2} + 23437500 x + 7031250} + \frac{109032 \log{\left (5 x + 3 \right )}}{1953125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-324*x**6/125 - 324*x**5/3125 + 22977*x**4/6250 - 393*x**3/625 - 62097*x**2/3125
0 + 424432*x/390625 - (38478*x + 23353)/(19531250*x**2 + 23437500*x + 7031250) +
109032*log(5*x + 3)/1953125

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GIAC/XCAS [A]  time = 0.209003, size = 70, normalized size = 0.96 \[ -\frac{324}{125} \, x^{6} - \frac{324}{3125} \, x^{5} + \frac{22977}{6250} \, x^{4} - \frac{393}{625} \, x^{3} - \frac{62097}{31250} \, x^{2} + \frac{424432}{390625} \, x - \frac{121 \,{\left (318 \, x + 193\right )}}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{109032}{1953125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-324/125*x^6 - 324/3125*x^5 + 22977/6250*x^4 - 393/625*x^3 - 62097/31250*x^2 + 4
24432/390625*x - 121/781250*(318*x + 193)/(5*x + 3)^2 + 109032/1953125*ln(abs(5*
x + 3))