3.1396 \(\int \frac{(1-2 x)^3}{(2+3 x)^4 (3+5 x)^2} \, dx\)

Optimal. Leaf size=57 \[ -\frac{2541}{3 x+2}-\frac{1331}{5 x+3}-\frac{1568}{9 (3 x+2)^2}-\frac{343}{27 (3 x+2)^3}+16698 \log (3 x+2)-16698 \log (5 x+3) \]

[Out]

-343/(27*(2 + 3*x)^3) - 1568/(9*(2 + 3*x)^2) - 2541/(2 + 3*x) - 1331/(3 + 5*x) +
16698*Log[2 + 3*x] - 16698*Log[3 + 5*x]

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Rubi [A]  time = 0.0691518, antiderivative size = 57, 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 \[ -\frac{2541}{3 x+2}-\frac{1331}{5 x+3}-\frac{1568}{9 (3 x+2)^2}-\frac{343}{27 (3 x+2)^3}+16698 \log (3 x+2)-16698 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-343/(27*(2 + 3*x)^3) - 1568/(9*(2 + 3*x)^2) - 2541/(2 + 3*x) - 1331/(3 + 5*x) +
16698*Log[2 + 3*x] - 16698*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 4.68658, size = 49, normalized size = 0.86 \[ 16698 \log{\left (3 x + 2 \right )} - 16698 \log{\left (5 x + 3 \right )} - \frac{1331}{5 x + 3} - \frac{2541}{3 x + 2} - \frac{1568}{9 \left (3 x + 2\right )^{2}} - \frac{343}{27 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

16698*log(3*x + 2) - 16698*log(5*x + 3) - 1331/(5*x + 3) - 2541/(3*x + 2) - 1568
/(9*(3*x + 2)**2) - 343/(27*(3*x + 2)**3)

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Mathematica [A]  time = 0.0471501, size = 59, normalized size = 1.04 \[ -\frac{2541}{3 x+2}-\frac{1331}{5 x+3}-\frac{1568}{9 (3 x+2)^2}-\frac{343}{27 (3 x+2)^3}+16698 \log (5 (3 x+2))-16698 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

-343/(27*(2 + 3*x)^3) - 1568/(9*(2 + 3*x)^2) - 2541/(2 + 3*x) - 1331/(3 + 5*x) +
16698*Log[5*(2 + 3*x)] - 16698*Log[3 + 5*x]

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Maple [A]  time = 0.014, size = 54, normalized size = 1. \[ -{\frac{343}{27\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{1568}{9\, \left ( 2+3\,x \right ) ^{2}}}-2541\, \left ( 2+3\,x \right ) ^{-1}-1331\, \left ( 3+5\,x \right ) ^{-1}+16698\,\ln \left ( 2+3\,x \right ) -16698\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-343/27/(2+3*x)^3-1568/9/(2+3*x)^2-2541/(2+3*x)-1331/(3+5*x)+16698*ln(2+3*x)-166
98*ln(3+5*x)

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Maxima [A]  time = 1.3337, size = 76, normalized size = 1.33 \[ -\frac{4057614 \, x^{3} + 7979967 \, x^{2} + 5226815 \, x + 1140033}{27 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} - 16698 \, \log \left (5 \, x + 3\right ) + 16698 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/27*(4057614*x^3 + 7979967*x^2 + 5226815*x + 1140033)/(135*x^4 + 351*x^3 + 342
*x^2 + 148*x + 24) - 16698*log(5*x + 3) + 16698*log(3*x + 2)

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Fricas [A]  time = 0.231965, size = 128, normalized size = 2.25 \[ -\frac{4057614 \, x^{3} + 7979967 \, x^{2} + 450846 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (5 \, x + 3\right ) - 450846 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (3 \, x + 2\right ) + 5226815 \, x + 1140033}{27 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/27*(4057614*x^3 + 7979967*x^2 + 450846*(135*x^4 + 351*x^3 + 342*x^2 + 148*x +
24)*log(5*x + 3) - 450846*(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)*log(3*x +
2) + 5226815*x + 1140033)/(135*x^4 + 351*x^3 + 342*x^2 + 148*x + 24)

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Sympy [A]  time = 0.473458, size = 51, normalized size = 0.89 \[ - \frac{4057614 x^{3} + 7979967 x^{2} + 5226815 x + 1140033}{3645 x^{4} + 9477 x^{3} + 9234 x^{2} + 3996 x + 648} - 16698 \log{\left (x + \frac{3}{5} \right )} + 16698 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(4057614*x**3 + 7979967*x**2 + 5226815*x + 1140033)/(3645*x**4 + 9477*x**3 + 92
34*x**2 + 3996*x + 648) - 16698*log(x + 3/5) + 16698*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.213169, size = 78, normalized size = 1.37 \[ -\frac{1331}{5 \, x + 3} + \frac{35 \,{\left (\frac{11119}{5 \, x + 3} + \frac{2244}{{\left (5 \, x + 3\right )}^{2}} + 14386\right )}}{{\left (\frac{1}{5 \, x + 3} + 3\right )}^{3}} + 16698 \,{\rm ln}\left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1331/(5*x + 3) + 35*(11119/(5*x + 3) + 2244/(5*x + 3)^2 + 14386)/(1/(5*x + 3) +
3)^3 + 16698*ln(abs(-1/(5*x + 3) - 3))