3.1412 \(\int \frac{(1-2 x)^3}{(2+3 x)^4 (3+5 x)^3} \, dx\)

Optimal. Leaf size=68 \[ \frac{15708}{3 x+2}+\frac{16698}{5 x+3}+\frac{1617}{2 (3 x+2)^2}-\frac{1331}{2 (5 x+3)^2}+\frac{343}{9 (3 x+2)^3}-128634 \log (3 x+2)+128634 \log (5 x+3) \]

[Out]

343/(9*(2 + 3*x)^3) + 1617/(2*(2 + 3*x)^2) + 15708/(2 + 3*x) - 1331/(2*(3 + 5*x)
^2) + 16698/(3 + 5*x) - 128634*Log[2 + 3*x] + 128634*Log[3 + 5*x]

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Rubi [A]  time = 0.081604, antiderivative size = 68, 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 \[ \frac{15708}{3 x+2}+\frac{16698}{5 x+3}+\frac{1617}{2 (3 x+2)^2}-\frac{1331}{2 (5 x+3)^2}+\frac{343}{9 (3 x+2)^3}-128634 \log (3 x+2)+128634 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(9*(2 + 3*x)^3) + 1617/(2*(2 + 3*x)^2) + 15708/(2 + 3*x) - 1331/(2*(3 + 5*x)
^2) + 16698/(3 + 5*x) - 128634*Log[2 + 3*x] + 128634*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 10.9805, size = 60, normalized size = 0.88 \[ - 128634 \log{\left (3 x + 2 \right )} + 128634 \log{\left (5 x + 3 \right )} + \frac{16698}{5 x + 3} - \frac{1331}{2 \left (5 x + 3\right )^{2}} + \frac{15708}{3 x + 2} + \frac{1617}{2 \left (3 x + 2\right )^{2}} + \frac{343}{9 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-128634*log(3*x + 2) + 128634*log(5*x + 3) + 16698/(5*x + 3) - 1331/(2*(5*x + 3)
**2) + 15708/(3*x + 2) + 1617/(2*(3*x + 2)**2) + 343/(9*(3*x + 2)**3)

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Mathematica [A]  time = 0.0534768, size = 70, normalized size = 1.03 \[ \frac{15708}{3 x+2}+\frac{16698}{5 x+3}+\frac{1617}{2 (3 x+2)^2}-\frac{1331}{2 (5 x+3)^2}+\frac{343}{9 (3 x+2)^3}-128634 \log (5 (3 x+2))+128634 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(9*(2 + 3*x)^3) + 1617/(2*(2 + 3*x)^2) + 15708/(2 + 3*x) - 1331/(2*(3 + 5*x)
^2) + 16698/(3 + 5*x) - 128634*Log[5*(2 + 3*x)] + 128634*Log[3 + 5*x]

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Maple [A]  time = 0.014, size = 63, normalized size = 0.9 \[{\frac{343}{9\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1617}{2\, \left ( 2+3\,x \right ) ^{2}}}+15708\, \left ( 2+3\,x \right ) ^{-1}-{\frac{1331}{2\, \left ( 3+5\,x \right ) ^{2}}}+16698\, \left ( 3+5\,x \right ) ^{-1}-128634\,\ln \left ( 2+3\,x \right ) +128634\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/9/(2+3*x)^3+1617/2/(2+3*x)^2+15708/(2+3*x)-1331/2/(3+5*x)^2+16698/(3+5*x)-12
8634*ln(2+3*x)+128634*ln(3+5*x)

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Maxima [A]  time = 1.34442, size = 89, normalized size = 1.31 \[ \frac{104193540 \, x^{4} + 267430086 \, x^{3} + 257165096 \, x^{2} + 109804551 \, x + 17564616}{18 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} + 128634 \, \log \left (5 \, x + 3\right ) - 128634 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/18*(104193540*x^4 + 267430086*x^3 + 257165096*x^2 + 109804551*x + 17564616)/(6
75*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72) + 128634*log(5*x + 3) - 12
8634*log(3*x + 2)

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Fricas [A]  time = 0.21593, size = 155, normalized size = 2.28 \[ \frac{104193540 \, x^{4} + 267430086 \, x^{3} + 257165096 \, x^{2} + 2315412 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 2315412 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (3 \, x + 2\right ) + 109804551 \, x + 17564616}{18 \,{\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/18*(104193540*x^4 + 267430086*x^3 + 257165096*x^2 + 2315412*(675*x^5 + 2160*x^
4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log(5*x + 3) - 2315412*(675*x^5 + 2160*x^4
+ 2763*x^3 + 1766*x^2 + 564*x + 72)*log(3*x + 2) + 109804551*x + 17564616)/(675
*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)

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Sympy [A]  time = 0.534217, size = 61, normalized size = 0.9 \[ \frac{104193540 x^{4} + 267430086 x^{3} + 257165096 x^{2} + 109804551 x + 17564616}{12150 x^{5} + 38880 x^{4} + 49734 x^{3} + 31788 x^{2} + 10152 x + 1296} + 128634 \log{\left (x + \frac{3}{5} \right )} - 128634 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(104193540*x**4 + 267430086*x**3 + 257165096*x**2 + 109804551*x + 17564616)/(121
50*x**5 + 38880*x**4 + 49734*x**3 + 31788*x**2 + 10152*x + 1296) + 128634*log(x
+ 3/5) - 128634*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.213404, size = 74, normalized size = 1.09 \[ \frac{104193540 \, x^{4} + 267430086 \, x^{3} + 257165096 \, x^{2} + 109804551 \, x + 17564616}{18 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{3}} + 128634 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 128634 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/18*(104193540*x^4 + 267430086*x^3 + 257165096*x^2 + 109804551*x + 17564616)/((
5*x + 3)^2*(3*x + 2)^3) + 128634*ln(abs(5*x + 3)) - 128634*ln(abs(3*x + 2))