3.1503 \(\int \frac{(2+3 x)^4}{(1-2 x) (3+5 x)^3} \, dx\)

Optimal. Leaf size=48 \[ -\frac{81 x}{250}-\frac{134}{75625 (5 x+3)}-\frac{1}{13750 (5 x+3)^2}-\frac{2401 \log (1-2 x)}{5324}+\frac{6802 \log (5 x+3)}{831875} \]

[Out]

(-81*x)/250 - 1/(13750*(3 + 5*x)^2) - 134/(75625*(3 + 5*x)) - (2401*Log[1 - 2*x]
)/5324 + (6802*Log[3 + 5*x])/831875

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Rubi [A]  time = 0.0536621, antiderivative size = 48, 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 \[ -\frac{81 x}{250}-\frac{134}{75625 (5 x+3)}-\frac{1}{13750 (5 x+3)^2}-\frac{2401 \log (1-2 x)}{5324}+\frac{6802 \log (5 x+3)}{831875} \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)^3),x]

[Out]

(-81*x)/250 - 1/(13750*(3 + 5*x)^2) - 134/(75625*(3 + 5*x)) - (2401*Log[1 - 2*x]
)/5324 + (6802*Log[3 + 5*x])/831875

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{2401 \log{\left (- 2 x + 1 \right )}}{5324} + \frac{6802 \log{\left (5 x + 3 \right )}}{831875} + \int \left (- \frac{81}{250}\right )\, dx - \frac{134}{75625 \left (5 x + 3\right )} - \frac{1}{13750 \left (5 x + 3\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**4/(1-2*x)/(3+5*x)**3,x)

[Out]

-2401*log(-2*x + 1)/5324 + 6802*log(5*x + 3)/831875 + Integral(-81/250, x) - 134
/(75625*(5*x + 3)) - 1/(13750*(5*x + 3)**2)

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Mathematica [A]  time = 0.0450539, size = 45, normalized size = 0.94 \[ \frac{-\frac{55 \left (490050 x^3+343035 x^2-117076 x-87883\right )}{(5 x+3)^2}-1500625 \log (1-2 x)+27208 \log (10 x+6)}{3327500} \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^4/((1 - 2*x)*(3 + 5*x)^3),x]

[Out]

((-55*(-87883 - 117076*x + 343035*x^2 + 490050*x^3))/(3 + 5*x)^2 - 1500625*Log[1
- 2*x] + 27208*Log[6 + 10*x])/3327500

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Maple [A]  time = 0.013, size = 39, normalized size = 0.8 \[ -{\frac{81\,x}{250}}-{\frac{1}{13750\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{134}{226875+378125\,x}}+{\frac{6802\,\ln \left ( 3+5\,x \right ) }{831875}}-{\frac{2401\,\ln \left ( -1+2\,x \right ) }{5324}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^4/(1-2*x)/(3+5*x)^3,x)

[Out]

-81/250*x-1/13750/(3+5*x)^2-134/75625/(3+5*x)+6802/831875*ln(3+5*x)-2401/5324*ln
(-1+2*x)

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Maxima [A]  time = 1.34323, size = 53, normalized size = 1.1 \[ -\frac{81}{250} \, x - \frac{268 \, x + 163}{30250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{6802}{831875} \, \log \left (5 \, x + 3\right ) - \frac{2401}{5324} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4/((5*x + 3)^3*(2*x - 1)),x, algorithm="maxima")

[Out]

-81/250*x - 1/30250*(268*x + 163)/(25*x^2 + 30*x + 9) + 6802/831875*log(5*x + 3)
- 2401/5324*log(2*x - 1)

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Fricas [A]  time = 0.215959, size = 88, normalized size = 1.83 \[ -\frac{26952750 \, x^{3} + 32343300 \, x^{2} - 27208 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 1500625 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 9732470 \, x + 17930}{3327500 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4/((5*x + 3)^3*(2*x - 1)),x, algorithm="fricas")

[Out]

-1/3327500*(26952750*x^3 + 32343300*x^2 - 27208*(25*x^2 + 30*x + 9)*log(5*x + 3)
+ 1500625*(25*x^2 + 30*x + 9)*log(2*x - 1) + 9732470*x + 17930)/(25*x^2 + 30*x
+ 9)

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Sympy [A]  time = 0.451013, size = 39, normalized size = 0.81 \[ - \frac{81 x}{250} - \frac{268 x + 163}{756250 x^{2} + 907500 x + 272250} - \frac{2401 \log{\left (x - \frac{1}{2} \right )}}{5324} + \frac{6802 \log{\left (x + \frac{3}{5} \right )}}{831875} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**4/(1-2*x)/(3+5*x)**3,x)

[Out]

-81*x/250 - (268*x + 163)/(756250*x**2 + 907500*x + 272250) - 2401*log(x - 1/2)/
5324 + 6802*log(x + 3/5)/831875

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GIAC/XCAS [A]  time = 0.217233, size = 49, normalized size = 1.02 \[ -\frac{81}{250} \, x - \frac{268 \, x + 163}{30250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{6802}{831875} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{2401}{5324} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^4/((5*x + 3)^3*(2*x - 1)),x, algorithm="giac")

[Out]

-81/250*x - 1/30250*(268*x + 163)/(5*x + 3)^2 + 6802/831875*ln(abs(5*x + 3)) - 2
401/5324*ln(abs(2*x - 1))