3.1581 \(\int \frac{1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)} \, dx\)

Optimal. Leaf size=53 \[ \frac{4}{539 (1-2 x)}+\frac{9}{49 (3 x+2)}-\frac{404 \log (1-2 x)}{41503}-\frac{351}{343} \log (3 x+2)+\frac{125}{121} \log (5 x+3) \]

[Out]

4/(539*(1 - 2*x)) + 9/(49*(2 + 3*x)) - (404*Log[1 - 2*x])/41503 - (351*Log[2 + 3
*x])/343 + (125*Log[3 + 5*x])/121

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Rubi [A]  time = 0.0633394, antiderivative size = 53, 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 \[ \frac{4}{539 (1-2 x)}+\frac{9}{49 (3 x+2)}-\frac{404 \log (1-2 x)}{41503}-\frac{351}{343} \log (3 x+2)+\frac{125}{121} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

4/(539*(1 - 2*x)) + 9/(49*(2 + 3*x)) - (404*Log[1 - 2*x])/41503 - (351*Log[2 + 3
*x])/343 + (125*Log[3 + 5*x])/121

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Rubi in Sympy [A]  time = 8.79973, size = 42, normalized size = 0.79 \[ - \frac{404 \log{\left (- 2 x + 1 \right )}}{41503} - \frac{351 \log{\left (3 x + 2 \right )}}{343} + \frac{125 \log{\left (5 x + 3 \right )}}{121} + \frac{9}{49 \left (3 x + 2\right )} + \frac{4}{539 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-404*log(-2*x + 1)/41503 - 351*log(3*x + 2)/343 + 125*log(5*x + 3)/121 + 9/(49*(
3*x + 2)) + 4/(539*(-2*x + 1))

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Mathematica [A]  time = 0.051235, size = 56, normalized size = 1.06 \[ \frac{\frac{14322 x}{6 x^2+x-2}-\frac{8239}{6 x^2+x-2}-404 \log (5-10 x)-42471 \log (5 (3 x+2))+42875 \log (5 x+3)}{41503} \]

Antiderivative was successfully verified.

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

[Out]

(-8239/(-2 + x + 6*x^2) + (14322*x)/(-2 + x + 6*x^2) - 404*Log[5 - 10*x] - 42471
*Log[5*(2 + 3*x)] + 42875*Log[3 + 5*x])/41503

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Maple [A]  time = 0.016, size = 44, normalized size = 0.8 \[{\frac{125\,\ln \left ( 3+5\,x \right ) }{121}}+{\frac{9}{98+147\,x}}-{\frac{351\,\ln \left ( 2+3\,x \right ) }{343}}-{\frac{4}{-539+1078\,x}}-{\frac{404\,\ln \left ( -1+2\,x \right ) }{41503}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/121*ln(3+5*x)+9/49/(2+3*x)-351/343*ln(2+3*x)-4/539/(-1+2*x)-404/41503*ln(-1+
2*x)

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Maxima [A]  time = 1.41584, size = 57, normalized size = 1.08 \[ \frac{186 \, x - 107}{539 \,{\left (6 \, x^{2} + x - 2\right )}} + \frac{125}{121} \, \log \left (5 \, x + 3\right ) - \frac{351}{343} \, \log \left (3 \, x + 2\right ) - \frac{404}{41503} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/539*(186*x - 107)/(6*x^2 + x - 2) + 125/121*log(5*x + 3) - 351/343*log(3*x + 2
) - 404/41503*log(2*x - 1)

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Fricas [A]  time = 0.225073, size = 88, normalized size = 1.66 \[ \frac{42875 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (5 \, x + 3\right ) - 42471 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (3 \, x + 2\right ) - 404 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (2 \, x - 1\right ) + 14322 \, x - 8239}{41503 \,{\left (6 \, x^{2} + x - 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/41503*(42875*(6*x^2 + x - 2)*log(5*x + 3) - 42471*(6*x^2 + x - 2)*log(3*x + 2)
- 404*(6*x^2 + x - 2)*log(2*x - 1) + 14322*x - 8239)/(6*x^2 + x - 2)

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Sympy [A]  time = 0.46624, size = 44, normalized size = 0.83 \[ \frac{186 x - 107}{3234 x^{2} + 539 x - 1078} - \frac{404 \log{\left (x - \frac{1}{2} \right )}}{41503} + \frac{125 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{351 \log{\left (x + \frac{2}{3} \right )}}{343} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(186*x - 107)/(3234*x**2 + 539*x - 1078) - 404*log(x - 1/2)/41503 + 125*log(x +
3/5)/121 - 351*log(x + 2/3)/343

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GIAC/XCAS [A]  time = 0.208071, size = 74, normalized size = 1.4 \[ \frac{9}{49 \,{\left (3 \, x + 2\right )}} + \frac{24}{3773 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}} + \frac{125}{121} \,{\rm ln}\left ({\left | -\frac{1}{3 \, x + 2} + 5 \right |}\right ) - \frac{404}{41503} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

9/49/(3*x + 2) + 24/3773/(7/(3*x + 2) - 2) + 125/121*ln(abs(-1/(3*x + 2) + 5)) -
404/41503*ln(abs(-7/(3*x + 2) + 2))