3.1672 \(\int \frac{(2+3 x)^3}{(1-2 x)^3 (3+5 x)^2} \, dx\)

Optimal. Leaf size=54 \[ -\frac{1421}{5324 (1-2 x)}-\frac{1}{6655 (5 x+3)}+\frac{343}{968 (1-2 x)^2}-\frac{21 \log (1-2 x)}{14641}+\frac{21 \log (5 x+3)}{14641} \]

[Out]

343/(968*(1 - 2*x)^2) - 1421/(5324*(1 - 2*x)) - 1/(6655*(3 + 5*x)) - (21*Log[1 -
2*x])/14641 + (21*Log[3 + 5*x])/14641

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Rubi [A]  time = 0.0635003, 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 \[ -\frac{1421}{5324 (1-2 x)}-\frac{1}{6655 (5 x+3)}+\frac{343}{968 (1-2 x)^2}-\frac{21 \log (1-2 x)}{14641}+\frac{21 \log (5 x+3)}{14641} \]

Antiderivative was successfully verified.

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

[Out]

343/(968*(1 - 2*x)^2) - 1421/(5324*(1 - 2*x)) - 1/(6655*(3 + 5*x)) - (21*Log[1 -
2*x])/14641 + (21*Log[3 + 5*x])/14641

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Rubi in Sympy [A]  time = 8.89175, size = 42, normalized size = 0.78 \[ - \frac{21 \log{\left (- 2 x + 1 \right )}}{14641} + \frac{21 \log{\left (5 x + 3 \right )}}{14641} - \frac{1}{6655 \left (5 x + 3\right )} - \frac{1421}{5324 \left (- 2 x + 1\right )} + \frac{343}{968 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-21*log(-2*x + 1)/14641 + 21*log(5*x + 3)/14641 - 1/(6655*(5*x + 3)) - 1421/(532
4*(-2*x + 1)) + 343/(968*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0592593, size = 47, normalized size = 0.87 \[ \frac{\frac{11 \left (142068 x^2+108567 x+13957\right )}{(1-2 x)^2 (5 x+3)}-840 \log (1-2 x)+840 \log (10 x+6)}{585640} \]

Antiderivative was successfully verified.

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

[Out]

((11*(13957 + 108567*x + 142068*x^2))/((1 - 2*x)^2*(3 + 5*x)) - 840*Log[1 - 2*x]
+ 840*Log[6 + 10*x])/585640

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Maple [A]  time = 0.015, size = 45, normalized size = 0.8 \[ -{\frac{1}{19965+33275\,x}}+{\frac{21\,\ln \left ( 3+5\,x \right ) }{14641}}+{\frac{343}{968\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{1421}{-5324+10648\,x}}-{\frac{21\,\ln \left ( -1+2\,x \right ) }{14641}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6655/(3+5*x)+21/14641*ln(3+5*x)+343/968/(-1+2*x)^2+1421/5324/(-1+2*x)-21/1464
1*ln(-1+2*x)

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Maxima [A]  time = 1.3656, size = 62, normalized size = 1.15 \[ \frac{142068 \, x^{2} + 108567 \, x + 13957}{53240 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{21}{14641} \, \log \left (5 \, x + 3\right ) - \frac{21}{14641} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/53240*(142068*x^2 + 108567*x + 13957)/(20*x^3 - 8*x^2 - 7*x + 3) + 21/14641*lo
g(5*x + 3) - 21/14641*log(2*x - 1)

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Fricas [A]  time = 0.2083, size = 101, normalized size = 1.87 \[ \frac{1562748 \, x^{2} + 840 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 840 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 1194237 \, x + 153527}{585640 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/585640*(1562748*x^2 + 840*(20*x^3 - 8*x^2 - 7*x + 3)*log(5*x + 3) - 840*(20*x^
3 - 8*x^2 - 7*x + 3)*log(2*x - 1) + 1194237*x + 153527)/(20*x^3 - 8*x^2 - 7*x +
3)

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Sympy [A]  time = 0.433132, size = 44, normalized size = 0.81 \[ \frac{142068 x^{2} + 108567 x + 13957}{1064800 x^{3} - 425920 x^{2} - 372680 x + 159720} - \frac{21 \log{\left (x - \frac{1}{2} \right )}}{14641} + \frac{21 \log{\left (x + \frac{3}{5} \right )}}{14641} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(142068*x**2 + 108567*x + 13957)/(1064800*x**3 - 425920*x**2 - 372680*x + 159720
) - 21*log(x - 1/2)/14641 + 21*log(x + 3/5)/14641

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GIAC/XCAS [A]  time = 0.211023, size = 69, normalized size = 1.28 \[ -\frac{1}{6655 \,{\left (5 \, x + 3\right )}} + \frac{245 \,{\left (\frac{66}{5 \, x + 3} + 23\right )}}{29282 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{21}{14641} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/6655/(5*x + 3) + 245/29282*(66/(5*x + 3) + 23)/(11/(5*x + 3) - 2)^2 - 21/1464
1*ln(abs(-11/(5*x + 3) + 2))