3.1501 \(\int \frac{(2+3 x)^6}{(1-2 x) (3+5 x)^3} \, dx\)

Optimal. Leaf size=62 \[ -\frac{243 x^3}{250}-\frac{19683 x^2}{5000}-\frac{216999 x}{25000}-\frac{8}{75625 (5 x+3)}-\frac{1}{343750 (5 x+3)^2}-\frac{117649 \log (1-2 x)}{21296}+\frac{3347 \log (5 x+3)}{4159375} \]

[Out]

(-216999*x)/25000 - (19683*x^2)/5000 - (243*x^3)/250 - 1/(343750*(3 + 5*x)^2) -
8/(75625*(3 + 5*x)) - (117649*Log[1 - 2*x])/21296 + (3347*Log[3 + 5*x])/4159375

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Rubi [A]  time = 0.0684709, antiderivative size = 62, 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 \[ -\frac{243 x^3}{250}-\frac{19683 x^2}{5000}-\frac{216999 x}{25000}-\frac{8}{75625 (5 x+3)}-\frac{1}{343750 (5 x+3)^2}-\frac{117649 \log (1-2 x)}{21296}+\frac{3347 \log (5 x+3)}{4159375} \]

Antiderivative was successfully verified.

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

[Out]

(-216999*x)/25000 - (19683*x^2)/5000 - (243*x^3)/250 - 1/(343750*(3 + 5*x)^2) -
8/(75625*(3 + 5*x)) - (117649*Log[1 - 2*x])/21296 + (3347*Log[3 + 5*x])/4159375

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{243 x^{3}}{250} - \frac{117649 \log{\left (- 2 x + 1 \right )}}{21296} + \frac{3347 \log{\left (5 x + 3 \right )}}{4159375} + \int \left (- \frac{216999}{25000}\right )\, dx - \frac{19683 \int x\, dx}{2500} - \frac{8}{75625 \left (5 x + 3\right )} - \frac{1}{343750 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x**3/250 - 117649*log(-2*x + 1)/21296 + 3347*log(5*x + 3)/4159375 + Integra
l(-216999/25000, x) - 19683*Integral(x, x)/2500 - 8/(75625*(5*x + 3)) - 1/(34375
0*(5*x + 3)**2)

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Mathematica [A]  time = 0.0968624, size = 56, normalized size = 0.9 \[ \frac{11 \left (-58806000 x^3-238164300 x^2-525137580 x-\frac{6400}{5 x+3}-\frac{176}{(5 x+3)^2}[phone]\right )-3676531250 \log (1-2 x)+535520 \log (10 x+6)}{665500000} \]

Antiderivative was successfully verified.

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

[Out]

(11*(329460615 - 525137580*x - 238164300*x^2 - 58806000*x^3 - 176/(3 + 5*x)^2 -
6400/(3 + 5*x)) - 3676531250*Log[1 - 2*x] + 535520*Log[6 + 10*x])/665500000

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Maple [A]  time = 0.013, size = 49, normalized size = 0.8 \[ -{\frac{243\,{x}^{3}}{250}}-{\frac{19683\,{x}^{2}}{5000}}-{\frac{216999\,x}{25000}}-{\frac{1}{343750\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{8}{226875+378125\,x}}+{\frac{3347\,\ln \left ( 3+5\,x \right ) }{4159375}}-{\frac{117649\,\ln \left ( -1+2\,x \right ) }{21296}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/250*x^3-19683/5000*x^2-216999/25000*x-1/343750/(3+5*x)^2-8/75625/(3+5*x)+33
47/4159375*ln(3+5*x)-117649/21296*ln(-1+2*x)

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Maxima [A]  time = 1.33357, size = 66, normalized size = 1.06 \[ -\frac{243}{250} \, x^{3} - \frac{19683}{5000} \, x^{2} - \frac{216999}{25000} \, x - \frac{2000 \, x + 1211}{3781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{3347}{4159375} \, \log \left (5 \, x + 3\right ) - \frac{117649}{21296} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/250*x^3 - 19683/5000*x^2 - 216999/25000*x - 1/3781250*(2000*x + 1211)/(25*x
^2 + 30*x + 9) + 3347/4159375*log(5*x + 3) - 117649/21296*log(2*x - 1)

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Fricas [A]  time = 0.210641, size = 101, normalized size = 1.63 \[ -\frac{8085825000 \, x^{5} + 42450581250 \, x^{4} + 114414423750 \, x^{3} + 98436833550 \, x^{2} - 267760 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 1838265625 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 25994486210 \, x + 106568}{332750000 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/332750000*(8085825000*x^5 + 42450581250*x^4 + 114414423750*x^3 + 98436833550*
x^2 - 267760*(25*x^2 + 30*x + 9)*log(5*x + 3) + 1838265625*(25*x^2 + 30*x + 9)*l
og(2*x - 1) + 25994486210*x + 106568)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.463771, size = 53, normalized size = 0.85 \[ - \frac{243 x^{3}}{250} - \frac{19683 x^{2}}{5000} - \frac{216999 x}{25000} - \frac{2000 x + 1211}{94531250 x^{2} + 113437500 x + 34031250} - \frac{117649 \log{\left (x - \frac{1}{2} \right )}}{21296} + \frac{3347 \log{\left (x + \frac{3}{5} \right )}}{4159375} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x**3/250 - 19683*x**2/5000 - 216999*x/25000 - (2000*x + 1211)/(94531250*x**
2 + 113437500*x + 34031250) - 117649*log(x - 1/2)/21296 + 3347*log(x + 3/5)/4159
375

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GIAC/XCAS [A]  time = 0.222311, size = 62, normalized size = 1. \[ -\frac{243}{250} \, x^{3} - \frac{19683}{5000} \, x^{2} - \frac{216999}{25000} \, x - \frac{2000 \, x + 1211}{3781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{3347}{4159375} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{117649}{21296} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/250*x^3 - 19683/5000*x^2 - 216999/25000*x - 1/3781250*(2000*x + 1211)/(5*x
+ 3)^2 + 3347/4159375*ln(abs(5*x + 3)) - 117649/21296*ln(abs(2*x - 1))