3.1411 \(\int \frac{(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=57 \[ \frac{1617}{3 x+2}+\frac{2541}{5 x+3}+\frac{343}{6 (3 x+2)^2}-\frac{1331}{10 (5 x+3)^2}-15708 \log (3 x+2)+15708 \log (5 x+3) \]

[Out]

343/(6*(2 + 3*x)^2) + 1617/(2 + 3*x) - 1331/(10*(3 + 5*x)^2) + 2541/(3 + 5*x) -
15708*Log[2 + 3*x] + 15708*Log[3 + 5*x]

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Rubi [A]  time = 0.0710593, 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 \[ \frac{1617}{3 x+2}+\frac{2541}{5 x+3}+\frac{343}{6 (3 x+2)^2}-\frac{1331}{10 (5 x+3)^2}-15708 \log (3 x+2)+15708 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(6*(2 + 3*x)^2) + 1617/(2 + 3*x) - 1331/(10*(3 + 5*x)^2) + 2541/(3 + 5*x) -
15708*Log[2 + 3*x] + 15708*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 9.73438, size = 49, normalized size = 0.86 \[ - 15708 \log{\left (3 x + 2 \right )} + 15708 \log{\left (5 x + 3 \right )} + \frac{2541}{5 x + 3} - \frac{1331}{10 \left (5 x + 3\right )^{2}} + \frac{1617}{3 x + 2} + \frac{343}{6 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-15708*log(3*x + 2) + 15708*log(5*x + 3) + 2541/(5*x + 3) - 1331/(10*(5*x + 3)**
2) + 1617/(3*x + 2) + 343/(6*(3*x + 2)**2)

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Mathematica [A]  time = 0.0537175, size = 59, normalized size = 1.04 \[ \frac{1617}{3 x+2}+\frac{2541}{5 x+3}+\frac{343}{6 (3 x+2)^2}-\frac{1331}{10 (5 x+3)^2}-15708 \log (5 (3 x+2))+15708 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(6*(2 + 3*x)^2) + 1617/(2 + 3*x) - 1331/(10*(3 + 5*x)^2) + 2541/(3 + 5*x) -
15708*Log[5*(2 + 3*x)] + 15708*Log[3 + 5*x]

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Maple [A]  time = 0.015, size = 54, normalized size = 1. \[{\frac{343}{6\, \left ( 2+3\,x \right ) ^{2}}}+1617\, \left ( 2+3\,x \right ) ^{-1}-{\frac{1331}{10\, \left ( 3+5\,x \right ) ^{2}}}+2541\, \left ( 3+5\,x \right ) ^{-1}-15708\,\ln \left ( 2+3\,x \right ) +15708\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/6/(2+3*x)^2+1617/(2+3*x)-1331/10/(3+5*x)^2+2541/(3+5*x)-15708*ln(2+3*x)+1570
8*ln(3+5*x)

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Maxima [A]  time = 1.34599, size = 76, normalized size = 1.33 \[ \frac{7068600 \, x^{3} + 13430348 \, x^{2} + 8492784 \, x + 1787403}{30 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + 15708 \, \log \left (5 \, x + 3\right ) - 15708 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/30*(7068600*x^3 + 13430348*x^2 + 8492784*x + 1787403)/(225*x^4 + 570*x^3 + 541
*x^2 + 228*x + 36) + 15708*log(5*x + 3) - 15708*log(3*x + 2)

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Fricas [A]  time = 0.217737, size = 128, normalized size = 2.25 \[ \frac{7068600 \, x^{3} + 13430348 \, x^{2} + 471240 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 471240 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 8492784 \, x + 1787403}{30 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/30*(7068600*x^3 + 13430348*x^2 + 471240*(225*x^4 + 570*x^3 + 541*x^2 + 228*x +
36)*log(5*x + 3) - 471240*(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)*log(3*x +
2) + 8492784*x + 1787403)/(225*x^4 + 570*x^3 + 541*x^2 + 228*x + 36)

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Sympy [A]  time = 0.435857, size = 51, normalized size = 0.89 \[ \frac{7068600 x^{3} + 13430348 x^{2} + 8492784 x + 1787403}{6750 x^{4} + 17100 x^{3} + 16230 x^{2} + 6840 x + 1080} + 15708 \log{\left (x + \frac{3}{5} \right )} - 15708 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(7068600*x**3 + 13430348*x**2 + 8492784*x + 1787403)/(6750*x**4 + 17100*x**3 + 1
6230*x**2 + 6840*x + 1080) + 15708*log(x + 3/5) - 15708*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.214559, size = 65, normalized size = 1.14 \[ \frac{7068600 \, x^{3} + 13430348 \, x^{2} + 8492784 \, x + 1787403}{30 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}^{2}} + 15708 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 15708 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/30*(7068600*x^3 + 13430348*x^2 + 8492784*x + 1787403)/(15*x^2 + 19*x + 6)^2 +
15708*ln(abs(5*x + 3)) - 15708*ln(abs(3*x + 2))