3.1299 \(\int \frac{(1-2 x)^2}{(2+3 x)^4 (3+5 x)^2} \, dx\)

Optimal. Leaf size=55 \[ -\frac{1133}{3 x+2}-\frac{605}{5 x+3}-\frac{77}{(3 x+2)^2}-\frac{49}{9 (3 x+2)^3}+7480 \log (3 x+2)-7480 \log (5 x+3) \]

[Out]

-49/(9*(2 + 3*x)^3) - 77/(2 + 3*x)^2 - 1133/(2 + 3*x) - 605/(3 + 5*x) + 7480*Log
[2 + 3*x] - 7480*Log[3 + 5*x]

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Rubi [A]  time = 0.068893, antiderivative size = 55, 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 \[ -\frac{1133}{3 x+2}-\frac{605}{5 x+3}-\frac{77}{(3 x+2)^2}-\frac{49}{9 (3 x+2)^3}+7480 \log (3 x+2)-7480 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-49/(9*(2 + 3*x)^3) - 77/(2 + 3*x)^2 - 1133/(2 + 3*x) - 605/(3 + 5*x) + 7480*Log
[2 + 3*x] - 7480*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 9.90074, size = 48, normalized size = 0.87 \[ 7480 \log{\left (3 x + 2 \right )} - 7480 \log{\left (5 x + 3 \right )} - \frac{605}{5 x + 3} - \frac{1133}{3 x + 2} - \frac{77}{\left (3 x + 2\right )^{2}} - \frac{49}{9 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

7480*log(3*x + 2) - 7480*log(5*x + 3) - 605/(5*x + 3) - 1133/(3*x + 2) - 77/(3*x
+ 2)**2 - 49/(9*(3*x + 2)**3)

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Mathematica [A]  time = 0.0507503, size = 57, normalized size = 1.04 \[ -\frac{1133}{3 x+2}-\frac{605}{5 x+3}-\frac{77}{(3 x+2)^2}-\frac{49}{9 (3 x+2)^3}+7480 \log (5 (3 x+2))-7480 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-49/(9*(2 + 3*x)^3) - 77/(2 + 3*x)^2 - 1133/(2 + 3*x) - 605/(3 + 5*x) + 7480*Log
[5*(2 + 3*x)] - 7480*Log[3 + 5*x]

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Maple [A]  time = 0.014, size = 54, normalized size = 1. \[ -{\frac{49}{9\, \left ( 2+3\,x \right ) ^{3}}}-77\, \left ( 2+3\,x \right ) ^{-2}-1133\, \left ( 2+3\,x \right ) ^{-1}-605\, \left ( 3+5\,x \right ) ^{-1}+7480\,\ln \left ( 2+3\,x \right ) -7480\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-49/9/(2+3*x)^3-77/(2+3*x)^2-1133/(2+3*x)-605/(3+5*x)+7480*ln(2+3*x)-7480*ln(3+5
*x)

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Maxima [A]  time = 1.35143, size = 76, normalized size = 1.38 \[ -\frac{605880 \, x^{3} + 1191564 \, x^{2} + 780464 \, x + 170229}{9 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} - 7480 \, \log \left (5 \, x + 3\right ) + 7480 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/9*(605880*x^3 + 1191564*x^2 + 780464*x + 170229)/(135*x^4 + 351*x^3 + 342*x^2
+ 148*x + 24) - 7480*log(5*x + 3) + 7480*log(3*x + 2)

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Fricas [A]  time = 0.226807, size = 128, normalized size = 2.33 \[ -\frac{605880 \, x^{3} + 1191564 \, x^{2} + 67320 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (5 \, x + 3\right ) - 67320 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (3 \, x + 2\right ) + 780464 \, x + 170229}{9 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/9*(605880*x^3 + 1191564*x^2 + 67320*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24
)*log(5*x + 3) - 67320*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(3*x + 2) +
780464*x + 170229)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)

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Sympy [A]  time = 0.476535, size = 51, normalized size = 0.93 \[ - \frac{605880 x^{3} + 1191564 x^{2} + 780464 x + 170229}{1215 x^{4} + 3159 x^{3} + 3078 x^{2} + 1332 x + 216} - 7480 \log{\left (x + \frac{3}{5} \right )} + 7480 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(605880*x**3 + 1191564*x**2 + 780464*x + 170229)/(1215*x**4 + 3159*x**3 + 3078*
x**2 + 1332*x + 216) - 7480*log(x + 3/5) + 7480*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.210777, size = 78, normalized size = 1.42 \[ -\frac{605}{5 \, x + 3} + \frac{5 \,{\left (\frac{34464}{5 \, x + 3} + \frac{6934}{{\left (5 \, x + 3\right )}^{2}} + 44661\right )}}{{\left (\frac{1}{5 \, x + 3} + 3\right )}^{3}} + 7480 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-605/(5*x + 3) + 5*(34464/(5*x + 3) + 6934/(5*x + 3)^2 + 44661)/(1/(5*x + 3) + 3
)^3 + 7480*ln(abs(-1/(5*x + 3) - 3))