3.1657 \(\int \frac{(2+3 x)^5}{(1-2 x)^3 (3+5 x)} \, dx\)

Optimal. Leaf size=55 \[ -\frac{243 x^2}{80}-\frac{10287 x}{400}-\frac{156065}{1936 (1-2 x)}+\frac{16807}{704 (1-2 x)^2}-\frac{543655 \log (1-2 x)}{10648}+\frac{\log (5 x+3)}{166375} \]

[Out]

16807/(704*(1 - 2*x)^2) - 156065/(1936*(1 - 2*x)) - (10287*x)/400 - (243*x^2)/80
- (543655*Log[1 - 2*x])/10648 + Log[3 + 5*x]/166375

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Rubi [A]  time = 0.0622242, antiderivative size = 55, 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 \[ -\frac{243 x^2}{80}-\frac{10287 x}{400}-\frac{156065}{1936 (1-2 x)}+\frac{16807}{704 (1-2 x)^2}-\frac{543655 \log (1-2 x)}{10648}+\frac{\log (5 x+3)}{166375} \]

Antiderivative was successfully verified.

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

[Out]

16807/(704*(1 - 2*x)^2) - 156065/(1936*(1 - 2*x)) - (10287*x)/400 - (243*x^2)/80
- (543655*Log[1 - 2*x])/10648 + Log[3 + 5*x]/166375

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{543655 \log{\left (- 2 x + 1 \right )}}{10648} + \frac{\log{\left (5 x + 3 \right )}}{166375} + \int \left (- \frac{10287}{400}\right )\, dx - \frac{243 \int x\, dx}{40} - \frac{156065}{1936 \left (- 2 x + 1\right )} + \frac{16807}{704 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-543655*log(-2*x + 1)/10648 + log(5*x + 3)/166375 + Integral(-10287/400, x) - 24
3*Integral(x, x)/40 - 156065/(1936*(-2*x + 1)) + 16807/(704*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0618047, size = 55, normalized size = 1. \[ \frac{-1293732 (5 x+3)^2-47005596 (5 x+3)+\frac{858357500}{2 x-1}+\frac{254205875}{(1-2 x)^2}-543655000 \log (5-10 x)+64 \log (5 x+3)}{10648000} \]

Antiderivative was successfully verified.

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

[Out]

(254205875/(1 - 2*x)^2 + 858357500/(-1 + 2*x) - 47005596*(3 + 5*x) - 1293732*(3
+ 5*x)^2 - 543655000*Log[5 - 10*x] + 64*Log[3 + 5*x])/10648000

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Maple [A]  time = 0.013, size = 44, normalized size = 0.8 \[ -{\frac{243\,{x}^{2}}{80}}-{\frac{10287\,x}{400}}+{\frac{\ln \left ( 3+5\,x \right ) }{166375}}+{\frac{16807}{704\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{156065}{-1936+3872\,x}}-{\frac{543655\,\ln \left ( -1+2\,x \right ) }{10648}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/80*x^2-10287/400*x+1/166375*ln(3+5*x)+16807/704/(-1+2*x)^2+156065/1936/(-1+
2*x)-543655/10648*ln(-1+2*x)

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Maxima [A]  time = 1.36063, size = 59, normalized size = 1.07 \[ -\frac{243}{80} \, x^{2} - \frac{10287}{400} \, x + \frac{2401 \,{\left (520 \, x - 183\right )}}{7744 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{1}{166375} \, \log \left (5 \, x + 3\right ) - \frac{543655}{10648} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/80*x^2 - 10287/400*x + 2401/7744*(520*x - 183)/(4*x^2 - 4*x + 1) + 1/166375
*log(5*x + 3) - 543655/10648*log(2*x - 1)

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Fricas [A]  time = 0.213962, size = 95, normalized size = 1.73 \[ -\frac{129373200 \, x^{4} + 965986560 \, x^{3} - 1063016460 \, x^{2} - 64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) + 543655000 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 1442875060 \, x + 604151625}{10648000 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/10648000*(129373200*x^4 + 965986560*x^3 - 1063016460*x^2 - 64*(4*x^2 - 4*x +
1)*log(5*x + 3) + 543655000*(4*x^2 - 4*x + 1)*log(2*x - 1) - 1442875060*x + 6041
51625)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.435335, size = 44, normalized size = 0.8 \[ - \frac{243 x^{2}}{80} - \frac{10287 x}{400} + \frac{1248520 x - 439383}{30976 x^{2} - 30976 x + 7744} - \frac{543655 \log{\left (x - \frac{1}{2} \right )}}{10648} + \frac{\log{\left (x + \frac{3}{5} \right )}}{166375} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x**2/80 - 10287*x/400 + (1248520*x - 439383)/(30976*x**2 - 30976*x + 7744)
- 543655*log(x - 1/2)/10648 + log(x + 3/5)/166375

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GIAC/XCAS [A]  time = 0.210615, size = 55, normalized size = 1. \[ -\frac{243}{80} \, x^{2} - \frac{10287}{400} \, x + \frac{2401 \,{\left (520 \, x - 183\right )}}{7744 \,{\left (2 \, x - 1\right )}^{2}} + \frac{1}{166375} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{543655}{10648} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/80*x^2 - 10287/400*x + 2401/7744*(520*x - 183)/(2*x - 1)^2 + 1/166375*ln(ab
s(5*x + 3)) - 543655/10648*ln(abs(2*x - 1))