3.1502 \(\int \frac{(2+3 x)^5}{(1-2 x) (3+5 x)^3} \, dx\)

Optimal. Leaf size=55 \[ -\frac{243 x^2}{500}-\frac{4941 x}{2500}-\frac{167}{378125 (5 x+3)}-\frac{1}{68750 (5 x+3)^2}-\frac{16807 \log (1-2 x)}{10648}+\frac{11224 \log (5 x+3)}{4159375} \]

[Out]

(-4941*x)/2500 - (243*x^2)/500 - 1/(68750*(3 + 5*x)^2) - 167/(378125*(3 + 5*x))
- (16807*Log[1 - 2*x])/10648 + (11224*Log[3 + 5*x])/4159375

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Rubi [A]  time = 0.0604598, 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 \[ -\frac{243 x^2}{500}-\frac{4941 x}{2500}-\frac{167}{378125 (5 x+3)}-\frac{1}{68750 (5 x+3)^2}-\frac{16807 \log (1-2 x)}{10648}+\frac{11224 \log (5 x+3)}{4159375} \]

Antiderivative was successfully verified.

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

[Out]

(-4941*x)/2500 - (243*x^2)/500 - 1/(68750*(3 + 5*x)^2) - 167/(378125*(3 + 5*x))
- (16807*Log[1 - 2*x])/10648 + (11224*Log[3 + 5*x])/4159375

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{16807 \log{\left (- 2 x + 1 \right )}}{10648} + \frac{11224 \log{\left (5 x + 3 \right )}}{4159375} + \int \left (- \frac{4941}{2500}\right )\, dx - \frac{243 \int x\, dx}{250} - \frac{167}{378125 \left (5 x + 3\right )} - \frac{1}{68750 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-16807*log(-2*x + 1)/10648 + 11224*log(5*x + 3)/4159375 + Integral(-4941/2500, x
) - 243*Integral(x, x)/250 - 167/(378125*(5*x + 3)) - 1/(68750*(5*x + 3)**2)

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Mathematica [A]  time = 0.0470839, size = 50, normalized size = 0.91 \[ \frac{-\frac{11 \left (73507500 x^4+387139500 x^3+217337175 x^2-93782210 x-60415061\right )}{(5 x+3)^2}-105043750 \log (1-2 x)+179584 \log (10 x+6)}{66550000} \]

Antiderivative was successfully verified.

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

[Out]

((-11*(-60415061 - 93782210*x + 217337175*x^2 + 387139500*x^3 + 73507500*x^4))/(
3 + 5*x)^2 - 105043750*Log[1 - 2*x] + 179584*Log[6 + 10*x])/66550000

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Maple [A]  time = 0.012, size = 44, normalized size = 0.8 \[ -{\frac{243\,{x}^{2}}{500}}-{\frac{4941\,x}{2500}}-{\frac{1}{68750\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{167}{1134375+1890625\,x}}+{\frac{11224\,\ln \left ( 3+5\,x \right ) }{4159375}}-{\frac{16807\,\ln \left ( -1+2\,x \right ) }{10648}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/500*x^2-4941/2500*x-1/68750/(3+5*x)^2-167/378125/(3+5*x)+11224/4159375*ln(3
+5*x)-16807/10648*ln(-1+2*x)

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Maxima [A]  time = 1.3491, size = 59, normalized size = 1.07 \[ -\frac{243}{500} \, x^{2} - \frac{4941}{2500} \, x - \frac{1670 \, x + 1013}{756250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{11224}{4159375} \, \log \left (5 \, x + 3\right ) - \frac{16807}{10648} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/500*x^2 - 4941/2500*x - 1/756250*(1670*x + 1013)/(25*x^2 + 30*x + 9) + 1122
4/4159375*log(5*x + 3) - 16807/10648*log(2*x - 1)

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Fricas [A]  time = 0.202412, size = 95, normalized size = 1.73 \[ -\frac{404291250 \, x^{4} + 2129267250 \, x^{3} + 2118486150 \, x^{2} - 89792 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 52521875 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 591955870 \, x + 44572}{33275000 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/33275000*(404291250*x^4 + 2129267250*x^3 + 2118486150*x^2 - 89792*(25*x^2 + 3
0*x + 9)*log(5*x + 3) + 52521875*(25*x^2 + 30*x + 9)*log(2*x - 1) + 591955870*x
+ 44572)/(25*x^2 + 30*x + 9)

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Sympy [A]  time = 0.449332, size = 46, normalized size = 0.84 \[ - \frac{243 x^{2}}{500} - \frac{4941 x}{2500} - \frac{1670 x + 1013}{18906250 x^{2} + 22687500 x + 6806250} - \frac{16807 \log{\left (x - \frac{1}{2} \right )}}{10648} + \frac{11224 \log{\left (x + \frac{3}{5} \right )}}{4159375} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243*x**2/500 - 4941*x/2500 - (1670*x + 1013)/(18906250*x**2 + 22687500*x + 6806
250) - 16807*log(x - 1/2)/10648 + 11224*log(x + 3/5)/4159375

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GIAC/XCAS [A]  time = 0.215069, size = 55, normalized size = 1. \[ -\frac{243}{500} \, x^{2} - \frac{4941}{2500} \, x - \frac{1670 \, x + 1013}{756250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{11224}{4159375} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{16807}{10648} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-243/500*x^2 - 4941/2500*x - 1/756250*(1670*x + 1013)/(5*x + 3)^2 + 11224/415937
5*ln(abs(5*x + 3)) - 16807/10648*ln(abs(2*x - 1))