3.1684 \(\int \frac{(2+3 x)^5}{(1-2 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=65 \[ -\frac{36015}{29282 (1-2 x)}-\frac{171}{1830125 (5 x+3)}+\frac{16807}{21296 (1-2 x)^2}-\frac{1}{332750 (5 x+3)^2}-\frac{313845 \log (1-2 x)}{1288408}+\frac{11904 \log (5 x+3)}{20131375} \]

[Out]

16807/(21296*(1 - 2*x)^2) - 36015/(29282*(1 - 2*x)) - 1/(332750*(3 + 5*x)^2) - 1
71/(1830125*(3 + 5*x)) - (313845*Log[1 - 2*x])/1288408 + (11904*Log[3 + 5*x])/20
131375

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Rubi [A]  time = 0.0762062, antiderivative size = 65, 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 \[ -\frac{36015}{29282 (1-2 x)}-\frac{171}{1830125 (5 x+3)}+\frac{16807}{21296 (1-2 x)^2}-\frac{1}{332750 (5 x+3)^2}-\frac{313845 \log (1-2 x)}{1288408}+\frac{11904 \log (5 x+3)}{20131375} \]

Antiderivative was successfully verified.

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

[Out]

16807/(21296*(1 - 2*x)^2) - 36015/(29282*(1 - 2*x)) - 1/(332750*(3 + 5*x)^2) - 1
71/(1830125*(3 + 5*x)) - (313845*Log[1 - 2*x])/1288408 + (11904*Log[3 + 5*x])/20
131375

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Rubi in Sympy [A]  time = 10.4043, size = 53, normalized size = 0.82 \[ - \frac{313845 \log{\left (- 2 x + 1 \right )}}{1288408} + \frac{11904 \log{\left (5 x + 3 \right )}}{20131375} - \frac{171}{1830125 \left (5 x + 3\right )} - \frac{1}{332750 \left (5 x + 3\right )^{2}} - \frac{36015}{29282 \left (- 2 x + 1\right )} + \frac{16807}{21296 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-313845*log(-2*x + 1)/1288408 + 11904*log(5*x + 3)/20131375 - 171/(1830125*(5*x
+ 3)) - 1/(332750*(5*x + 3)**2) - 36015/(29282*(-2*x + 1)) + 16807/(21296*(-2*x
+ 1)**2)

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Mathematica [A]  time = 0.0490937, size = 50, normalized size = 0.77 \[ \frac{\frac{11 \left (1800695280 x^3+1838287161 x^2+261128254 x-116156671\right )}{\left (10 x^2+x-3\right )^2}-78461250 \log (3-6 x)+190464 \log (-3 (5 x+3))}{322102000} \]

Antiderivative was successfully verified.

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

[Out]

((11*(-116156671 + 261128254*x + 1838287161*x^2 + 1800695280*x^3))/(-3 + x + 10*
x^2)^2 - 78461250*Log[3 - 6*x] + 190464*Log[-3*(3 + 5*x)])/322102000

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Maple [A]  time = 0.016, size = 54, normalized size = 0.8 \[ -{\frac{1}{332750\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{171}{5490375+9150625\,x}}+{\frac{11904\,\ln \left ( 3+5\,x \right ) }{20131375}}+{\frac{16807}{21296\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{36015}{-29282+58564\,x}}-{\frac{313845\,\ln \left ( -1+2\,x \right ) }{1288408}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/332750/(3+5*x)^2-171/1830125/(3+5*x)+11904/20131375*ln(3+5*x)+16807/21296/(-1
+2*x)^2+36015/29282/(-1+2*x)-313845/1288408*ln(-1+2*x)

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Maxima [A]  time = 1.35413, size = 76, normalized size = 1.17 \[ \frac{1800695280 \, x^{3} + 1838287161 \, x^{2} + 261128254 \, x - 116156671}{29282000 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{11904}{20131375} \, \log \left (5 \, x + 3\right ) - \frac{313845}{1288408} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/29282000*(1800695280*x^3 + 1838287161*x^2 + 261128254*x - 116156671)/(100*x^4
+ 20*x^3 - 59*x^2 - 6*x + 9) + 11904/20131375*log(5*x + 3) - 313845/1288408*log(
2*x - 1)

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Fricas [A]  time = 0.209995, size = 128, normalized size = 1.97 \[ \frac{19807648080 \, x^{3} + 20221158771 \, x^{2} + 190464 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 78461250 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 2872410794 \, x - 1277723381}{322102000 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/322102000*(19807648080*x^3 + 20221158771*x^2 + 190464*(100*x^4 + 20*x^3 - 59*x
^2 - 6*x + 9)*log(5*x + 3) - 78461250*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(
2*x - 1) + 2872410794*x - 1277723381)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)

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Sympy [A]  time = 0.53994, size = 54, normalized size = 0.83 \[ \frac{1800695280 x^{3} + 1838287161 x^{2} + 261128254 x - 116156671}{2928200000 x^{4} + 585640000 x^{3} - 1727638000 x^{2} - 175692000 x + 263538000} - \frac{313845 \log{\left (x - \frac{1}{2} \right )}}{1288408} + \frac{11904 \log{\left (x + \frac{3}{5} \right )}}{20131375} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(1800695280*x**3 + 1838287161*x**2 + 261128254*x - 116156671)/(2928200000*x**4 +
585640000*x**3 - 1727638000*x**2 - 175692000*x + 263538000) - 313845*log(x - 1/
2)/1288408 + 11904*log(x + 3/5)/20131375

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GIAC/XCAS [A]  time = 0.218465, size = 68, normalized size = 1.05 \[ \frac{1800695280 \, x^{3} + 1838287161 \, x^{2} + 261128254 \, x - 116156671}{29282000 \,{\left (5 \, x + 3\right )}^{2}{\left (2 \, x - 1\right )}^{2}} + \frac{11904}{20131375} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{313845}{1288408} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/29282000*(1800695280*x^3 + 1838287161*x^2 + 261128254*x - 116156671)/((5*x + 3
)^2*(2*x - 1)^2) + 11904/20131375*ln(abs(5*x + 3)) - 313845/1288408*ln(abs(2*x -
1))