3.1496 \(\int \frac{1}{(1-2 x) (2+3 x)^4 (3+5 x)^2} \, dx\)

Optimal. Leaf size=75 \[ -\frac{34371}{343 (3 x+2)}-\frac{625}{11 (5 x+3)}-\frac{324}{49 (3 x+2)^2}-\frac{3}{7 (3 x+2)^3}-\frac{32 \log (1-2 x)}{290521}+\frac{1612242 \log (3 x+2)}{2401}-\frac{81250}{121} \log (5 x+3) \]

[Out]

-3/(7*(2 + 3*x)^3) - 324/(49*(2 + 3*x)^2) - 34371/(343*(2 + 3*x)) - 625/(11*(3 +
5*x)) - (32*Log[1 - 2*x])/290521 + (1612242*Log[2 + 3*x])/2401 - (81250*Log[3 +
5*x])/121

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Rubi [A]  time = 0.0834564, antiderivative size = 75, 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 \[ -\frac{34371}{343 (3 x+2)}-\frac{625}{11 (5 x+3)}-\frac{324}{49 (3 x+2)^2}-\frac{3}{7 (3 x+2)^3}-\frac{32 \log (1-2 x)}{290521}+\frac{1612242 \log (3 x+2)}{2401}-\frac{81250}{121} \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-3/(7*(2 + 3*x)^3) - 324/(49*(2 + 3*x)^2) - 34371/(343*(2 + 3*x)) - 625/(11*(3 +
5*x)) - (32*Log[1 - 2*x])/290521 + (1612242*Log[2 + 3*x])/2401 - (81250*Log[3 +
5*x])/121

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Rubi in Sympy [A]  time = 11.3916, size = 63, normalized size = 0.84 \[ - \frac{32 \log{\left (- 2 x + 1 \right )}}{290521} + \frac{1612242 \log{\left (3 x + 2 \right )}}{2401} - \frac{81250 \log{\left (5 x + 3 \right )}}{121} - \frac{625}{11 \left (5 x + 3\right )} - \frac{34371}{343 \left (3 x + 2\right )} - \frac{324}{49 \left (3 x + 2\right )^{2}} - \frac{3}{7 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-32*log(-2*x + 1)/290521 + 1612242*log(3*x + 2)/2401 - 81250*log(5*x + 3)/121 -
625/(11*(5*x + 3)) - 34371/(343*(3*x + 2)) - 324/(49*(3*x + 2)**2) - 3/(7*(3*x +
2)**3)

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Mathematica [A]  time = 0.127245, size = 62, normalized size = 0.83 \[ \frac{2 \left (-\frac{77 \left (22801770 x^3+44843517 x^2+29372133 x+6406511\right )}{2 (3 x+2)^3 (5 x+3)}-16 \log (1-2 x)[phone] \log (6 x+4)-97540625 \log (10 x+6)\right )}{290521} \]

Antiderivative was successfully verified.

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

[Out]

(2*((-77*(6406511 + 29372133*x + 44843517*x^2 + 22801770*x^3))/(2*(2 + 3*x)^3*(3
+ 5*x)) - 16*Log[1 - 2*x] + 97540641*Log[4 + 6*x] - 97540625*Log[6 + 10*x]))/29
0521

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Maple [A]  time = 0.016, size = 62, normalized size = 0.8 \[ -{\frac{625}{33+55\,x}}-{\frac{81250\,\ln \left ( 3+5\,x \right ) }{121}}-{\frac{3}{7\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{324}{49\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{34371}{686+1029\,x}}+{\frac{1612242\,\ln \left ( 2+3\,x \right ) }{2401}}-{\frac{32\,\ln \left ( -1+2\,x \right ) }{290521}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-625/11/(3+5*x)-81250/121*ln(3+5*x)-3/7/(2+3*x)^3-324/49/(2+3*x)^2-34371/343/(2+
3*x)+1612242/2401*ln(2+3*x)-32/290521*ln(-1+2*x)

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Maxima [A]  time = 1.34164, size = 86, normalized size = 1.15 \[ -\frac{22801770 \, x^{3} + 44843517 \, x^{2} + 29372133 \, x + 6406511}{3773 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} - \frac{81250}{121} \, \log \left (5 \, x + 3\right ) + \frac{1612242}{2401} \, \log \left (3 \, x + 2\right ) - \frac{32}{290521} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3773*(22801770*x^3 + 44843517*x^2 + 29372133*x + 6406511)/(135*x^4 + 351*x^3
+ 342*x^2 + 148*x + 24) - 81250/121*log(5*x + 3) + 1612242/2401*log(3*x + 2) - 3
2/290521*log(2*x - 1)

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Fricas [A]  time = 0.220991, size = 166, normalized size = 2.21 \[ -\frac{1755736290 \, x^{3} + 3452950809 \, x^{2} + 195081250 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (5 \, x + 3\right ) - 195081282 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (3 \, x + 2\right ) + 32 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (2 \, x - 1\right ) + 2261654241 \, x + 493301347}{290521 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/290521*(1755736290*x^3 + 3452950809*x^2 + 195081250*(135*x^4 + 351*x^3 + 342*
x^2 + 148*x + 24)*log(5*x + 3) - 195081282*(135*x^4 + 351*x^3 + 342*x^2 + 148*x
+ 24)*log(3*x + 2) + 32*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(2*x - 1)
+ 2261654241*x + 493301347)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)

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Sympy [A]  time = 0.631599, size = 65, normalized size = 0.87 \[ - \frac{22801770 x^{3} + 44843517 x^{2} + 29372133 x + 6406511}{509355 x^{4} + 1324323 x^{3} + 1290366 x^{2} + 558404 x + 90552} - \frac{32 \log{\left (x - \frac{1}{2} \right )}}{290521} - \frac{81250 \log{\left (x + \frac{3}{5} \right )}}{121} + \frac{1612242 \log{\left (x + \frac{2}{3} \right )}}{2401} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(22801770*x**3 + 44843517*x**2 + 29372133*x + 6406511)/(509355*x**4 + 1324323*x
**3 + 1290366*x**2 + 558404*x + 90552) - 32*log(x - 1/2)/290521 - 81250*log(x +
3/5)/121 + 1612242*log(x + 2/3)/2401

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GIAC/XCAS [A]  time = 0.210252, size = 99, normalized size = 1.32 \[ -\frac{625}{11 \,{\left (5 \, x + 3\right )}} + \frac{135 \,{\left (\frac{37929}{5 \, x + 3} + \frac{7564}{{\left (5 \, x + 3\right )}^{2}} + 49386\right )}}{343 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{3}} + \frac{1612242}{2401} \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{32}{290521} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-625/11/(5*x + 3) + 135/343*(37929/(5*x + 3) + 7564/(5*x + 3)^2 + 49386)/(1/(5*x
+ 3) + 3)^3 + 1612242/2401*ln(abs(-1/(5*x + 3) - 3)) - 32/290521*ln(abs(-11/(5*
x + 3) + 2))