3.1604 \(\int \frac{(2+3 x)^4}{(1-2 x)^2 (3+5 x)^3} \, dx\)

Optimal. Leaf size=54 \[ \frac{2401}{5324 (1-2 x)}-\frac{136}{166375 (5 x+3)}-\frac{1}{30250 (5 x+3)^2}+\frac{9261 \log (1-2 x)}{58564}+\frac{7074 \log (5 x+3)}{1830125} \]

[Out]

2401/(5324*(1 - 2*x)) - 1/(30250*(3 + 5*x)^2) - 136/(166375*(3 + 5*x)) + (9261*L
og[1 - 2*x])/58564 + (7074*Log[3 + 5*x])/1830125

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Rubi [A]  time = 0.0616089, antiderivative size = 54, 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 \[ \frac{2401}{5324 (1-2 x)}-\frac{136}{166375 (5 x+3)}-\frac{1}{30250 (5 x+3)^2}+\frac{9261 \log (1-2 x)}{58564}+\frac{7074 \log (5 x+3)}{1830125} \]

Antiderivative was successfully verified.

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

[Out]

2401/(5324*(1 - 2*x)) - 1/(30250*(3 + 5*x)^2) - 136/(166375*(3 + 5*x)) + (9261*L
og[1 - 2*x])/58564 + (7074*Log[3 + 5*x])/1830125

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Rubi in Sympy [A]  time = 8.83618, size = 42, normalized size = 0.78 \[ \frac{9261 \log{\left (- 2 x + 1 \right )}}{58564} + \frac{7074 \log{\left (5 x + 3 \right )}}{1830125} - \frac{136}{166375 \left (5 x + 3\right )} - \frac{1}{30250 \left (5 x + 3\right )^{2}} + \frac{2401}{5324 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

9261*log(-2*x + 1)/58564 + 7074*log(5*x + 3)/1830125 - 136/(166375*(5*x + 3)) -
1/(30250*(5*x + 3)**2) + 2401/(5324*(-2*x + 1))

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Mathematica [A]  time = 0.0531213, size = 48, normalized size = 0.89 \[ \frac{\frac{3301375}{1-2 x}-\frac{5984}{5 x+3}-\frac{242}{(5 x+3)^2}+1157625 \log (1-2 x)+28296 \log (10 x+6)}{7320500} \]

Antiderivative was successfully verified.

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

[Out]

(3301375/(1 - 2*x) - 242/(3 + 5*x)^2 - 5984/(3 + 5*x) + 1157625*Log[1 - 2*x] + 2
8296*Log[6 + 10*x])/7320500

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Maple [A]  time = 0.015, size = 45, normalized size = 0.8 \[ -{\frac{1}{30250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{136}{499125+831875\,x}}+{\frac{7074\,\ln \left ( 3+5\,x \right ) }{1830125}}-{\frac{2401}{-5324+10648\,x}}+{\frac{9261\,\ln \left ( -1+2\,x \right ) }{58564}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/30250/(3+5*x)^2-136/166375/(3+5*x)+7074/1830125*ln(3+5*x)-2401/5324/(-1+2*x)+
9261/58564*ln(-1+2*x)

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Maxima [A]  time = 1.34709, size = 62, normalized size = 1.15 \[ -\frac{7508565 \, x^{2} + 9004338 \, x + 2699471}{665500 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{7074}{1830125} \, \log \left (5 \, x + 3\right ) + \frac{9261}{58564} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/665500*(7508565*x^2 + 9004338*x + 2699471)/(50*x^3 + 35*x^2 - 12*x - 9) + 707
4/1830125*log(5*x + 3) + 9261/58564*log(2*x - 1)

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Fricas [A]  time = 0.220758, size = 101, normalized size = 1.87 \[ -\frac{82594215 \, x^{2} - 28296 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) - 1157625 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) + 99047718 \, x + 29694181}{7320500 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/7320500*(82594215*x^2 - 28296*(50*x^3 + 35*x^2 - 12*x - 9)*log(5*x + 3) - 115
7625*(50*x^3 + 35*x^2 - 12*x - 9)*log(2*x - 1) + 99047718*x + 29694181)/(50*x^3
+ 35*x^2 - 12*x - 9)

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Sympy [A]  time = 0.451062, size = 44, normalized size = 0.81 \[ - \frac{7508565 x^{2} + 9004338 x + 2699471}{33275000 x^{3} + 23292500 x^{2} - 7986000 x - 5989500} + \frac{9261 \log{\left (x - \frac{1}{2} \right )}}{58564} + \frac{7074 \log{\left (x + \frac{3}{5} \right )}}{1830125} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(7508565*x**2 + 9004338*x + 2699471)/(33275000*x**3 + 23292500*x**2 - 7986000*x
- 5989500) + 9261*log(x - 1/2)/58564 + 7074*log(x + 3/5)/1830125

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GIAC/XCAS [A]  time = 0.208223, size = 93, normalized size = 1.72 \[ -\frac{2401}{5324 \,{\left (2 \, x - 1\right )}} + \frac{2 \,{\left (\frac{1518}{2 \, x - 1} + 685\right )}}{366025 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} - \frac{81}{500} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{7074}{1830125} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2401/5324/(2*x - 1) + 2/366025*(1518/(2*x - 1) + 685)/(11/(2*x - 1) + 5)^2 - 81
/500*ln(1/2*abs(2*x - 1)/(2*x - 1)^2) + 7074/1830125*ln(abs(-11/(2*x - 1) - 5))