3.1463 \(\int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^5} \, dx\)

Optimal. Leaf size=65 \[ -\frac{1331}{2401 (3 x+2)}+\frac{3469}{18522 (3 x+2)^2}-\frac{103}{3969 (3 x+2)^3}+\frac{1}{756 (3 x+2)^4}-\frac{2662 \log (1-2 x)}{16807}+\frac{2662 \log (3 x+2)}{16807} \]

[Out]

1/(756*(2 + 3*x)^4) - 103/(3969*(2 + 3*x)^3) + 3469/(18522*(2 + 3*x)^2) - 1331/(
2401*(2 + 3*x)) - (2662*Log[1 - 2*x])/16807 + (2662*Log[2 + 3*x])/16807

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Rubi [A]  time = 0.0667264, 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 \[ -\frac{1331}{2401 (3 x+2)}+\frac{3469}{18522 (3 x+2)^2}-\frac{103}{3969 (3 x+2)^3}+\frac{1}{756 (3 x+2)^4}-\frac{2662 \log (1-2 x)}{16807}+\frac{2662 \log (3 x+2)}{16807} \]

Antiderivative was successfully verified.

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

[Out]

1/(756*(2 + 3*x)^4) - 103/(3969*(2 + 3*x)^3) + 3469/(18522*(2 + 3*x)^2) - 1331/(
2401*(2 + 3*x)) - (2662*Log[1 - 2*x])/16807 + (2662*Log[2 + 3*x])/16807

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Rubi in Sympy [A]  time = 10.2171, size = 56, normalized size = 0.86 \[ - \frac{2662 \log{\left (- 2 x + 1 \right )}}{16807} + \frac{2662 \log{\left (3 x + 2 \right )}}{16807} - \frac{1331}{2401 \left (3 x + 2\right )} + \frac{3469}{18522 \left (3 x + 2\right )^{2}} - \frac{103}{3969 \left (3 x + 2\right )^{3}} + \frac{1}{756 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2662*log(-2*x + 1)/16807 + 2662*log(3*x + 2)/16807 - 1331/(2401*(3*x + 2)) + 34
69/(18522*(3*x + 2)**2) - 103/(3969*(3*x + 2)**3) + 1/(756*(3*x + 2)**4)

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Mathematica [A]  time = 0.055118, size = 47, normalized size = 0.72 \[ \frac{2 \left (-\frac{7 \left (11643588 x^3+21975894 x^2+13836972 x+2906507\right )}{8 (3 x+2)^4}-107811 \log (1-2 x)+107811 \log (6 x+4)\right )}{1361367} \]

Antiderivative was successfully verified.

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

[Out]

(2*((-7*(2906507 + 13836972*x + 21975894*x^2 + 11643588*x^3))/(8*(2 + 3*x)^4) -
107811*Log[1 - 2*x] + 107811*Log[4 + 6*x]))/1361367

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Maple [A]  time = 0.013, size = 54, normalized size = 0.8 \[{\frac{1}{756\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{103}{3969\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{3469}{18522\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{1331}{4802+7203\,x}}+{\frac{2662\,\ln \left ( 2+3\,x \right ) }{16807}}-{\frac{2662\,\ln \left ( -1+2\,x \right ) }{16807}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/756/(2+3*x)^4-103/3969/(2+3*x)^3+3469/18522/(2+3*x)^2-1331/2401/(2+3*x)+2662/1
6807*ln(2+3*x)-2662/16807*ln(-1+2*x)

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Maxima [A]  time = 1.34419, size = 76, normalized size = 1.17 \[ -\frac{11643588 \, x^{3} + 21975894 \, x^{2} + 13836972 \, x + 2906507}{777924 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{2662}{16807} \, \log \left (3 \, x + 2\right ) - \frac{2662}{16807} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/777924*(11643588*x^3 + 21975894*x^2 + 13836972*x + 2906507)/(81*x^4 + 216*x^3
+ 216*x^2 + 96*x + 16) + 2662/16807*log(3*x + 2) - 2662/16807*log(2*x - 1)

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Fricas [A]  time = 0.213562, size = 128, normalized size = 1.97 \[ -\frac{81505116 \, x^{3} + 153831258 \, x^{2} - 862488 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 862488 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (2 \, x - 1\right ) + 96858804 \, x + 20345549}{5445468 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/5445468*(81505116*x^3 + 153831258*x^2 - 862488*(81*x^4 + 216*x^3 + 216*x^2 +
96*x + 16)*log(3*x + 2) + 862488*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*log(2*
x - 1) + 96858804*x + 20345549)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)

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Sympy [A]  time = 0.475888, size = 54, normalized size = 0.83 \[ - \frac{11643588 x^{3} + 21975894 x^{2} + 13836972 x + 2906507}{63011844 x^{4} + 168031584 x^{3} + 168031584 x^{2} + 74680704 x + 12446784} - \frac{2662 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{2662 \log{\left (x + \frac{2}{3} \right )}}{16807} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(11643588*x**3 + 21975894*x**2 + 13836972*x + 2906507)/(63011844*x**4 + 1680315
84*x**3 + 168031584*x**2 + 74680704*x + 12446784) - 2662*log(x - 1/2)/16807 + 26
62*log(x + 2/3)/16807

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GIAC/XCAS [A]  time = 0.212277, size = 70, normalized size = 1.08 \[ -\frac{1331}{2401 \,{\left (3 \, x + 2\right )}} + \frac{3469}{18522 \,{\left (3 \, x + 2\right )}^{2}} - \frac{103}{3969 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1}{756 \,{\left (3 \, x + 2\right )}^{4}} - \frac{2662}{16807} \,{\rm ln}\left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1331/2401/(3*x + 2) + 3469/18522/(3*x + 2)^2 - 103/3969/(3*x + 2)^3 + 1/756/(3*
x + 2)^4 - 2662/16807*ln(abs(-7/(3*x + 2) + 2))