3.1381 \(\int \frac{(1-2 x)^3}{(2+3 x)^4 (3+5 x)} \, dx\)

Optimal. Leaf size=50 \[ \frac{7189}{27 (3 x+2)}+\frac{1421}{54 (3 x+2)^2}+\frac{343}{81 (3 x+2)^3}-1331 \log (3 x+2)+1331 \log (5 x+3) \]

[Out]

343/(81*(2 + 3*x)^3) + 1421/(54*(2 + 3*x)^2) + 7189/(27*(2 + 3*x)) - 1331*Log[2
+ 3*x] + 1331*Log[3 + 5*x]

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Rubi [A]  time = 0.0566312, antiderivative size = 50, 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 \[ \frac{7189}{27 (3 x+2)}+\frac{1421}{54 (3 x+2)^2}+\frac{343}{81 (3 x+2)^3}-1331 \log (3 x+2)+1331 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

343/(81*(2 + 3*x)^3) + 1421/(54*(2 + 3*x)^2) + 7189/(27*(2 + 3*x)) - 1331*Log[2
+ 3*x] + 1331*Log[3 + 5*x]

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Rubi in Sympy [A]  time = 8.42503, size = 42, normalized size = 0.84 \[ - 1331 \log{\left (3 x + 2 \right )} + 1331 \log{\left (5 x + 3 \right )} + \frac{7189}{27 \left (3 x + 2\right )} + \frac{1421}{54 \left (3 x + 2\right )^{2}} + \frac{343}{81 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1331*log(3*x + 2) + 1331*log(5*x + 3) + 7189/(27*(3*x + 2)) + 1421/(54*(3*x + 2
)**2) + 343/(81*(3*x + 2)**3)

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Mathematica [A]  time = 0.0450027, size = 40, normalized size = 0.8 \[ \frac{7 \left (55458 x^2+75771 x+25964\right )}{162 (3 x+2)^3}-1331 \log (5 (3 x+2))+1331 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

(7*(25964 + 75771*x + 55458*x^2))/(162*(2 + 3*x)^3) - 1331*Log[5*(2 + 3*x)] + 13
31*Log[3 + 5*x]

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Maple [A]  time = 0.011, size = 45, normalized size = 0.9 \[{\frac{343}{81\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1421}{54\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{7189}{54+81\,x}}-1331\,\ln \left ( 2+3\,x \right ) +1331\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/81/(2+3*x)^3+1421/54/(2+3*x)^2+7189/27/(2+3*x)-1331*ln(2+3*x)+1331*ln(3+5*x)

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Maxima [A]  time = 1.34679, size = 62, normalized size = 1.24 \[ \frac{7 \,{\left (55458 \, x^{2} + 75771 \, x + 25964\right )}}{162 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + 1331 \, \log \left (5 \, x + 3\right ) - 1331 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

7/162*(55458*x^2 + 75771*x + 25964)/(27*x^3 + 54*x^2 + 36*x + 8) + 1331*log(5*x
+ 3) - 1331*log(3*x + 2)

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Fricas [A]  time = 0.21747, size = 101, normalized size = 2.02 \[ \frac{388206 \, x^{2} + 215622 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 215622 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 530397 \, x + 181748}{162 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/162*(388206*x^2 + 215622*(27*x^3 + 54*x^2 + 36*x + 8)*log(5*x + 3) - 215622*(2
7*x^3 + 54*x^2 + 36*x + 8)*log(3*x + 2) + 530397*x + 181748)/(27*x^3 + 54*x^2 +
36*x + 8)

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Sympy [A]  time = 0.42678, size = 41, normalized size = 0.82 \[ \frac{388206 x^{2} + 530397 x + 181748}{4374 x^{3} + 8748 x^{2} + 5832 x + 1296} + 1331 \log{\left (x + \frac{3}{5} \right )} - 1331 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(388206*x**2 + 530397*x + 181748)/(4374*x**3 + 8748*x**2 + 5832*x + 1296) + 1331
*log(x + 3/5) - 1331*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.212659, size = 51, normalized size = 1.02 \[ \frac{7 \,{\left (55458 \, x^{2} + 75771 \, x + 25964\right )}}{162 \,{\left (3 \, x + 2\right )}^{3}} + 1331 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 1331 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

7/162*(55458*x^2 + 75771*x + 25964)/(3*x + 2)^3 + 1331*ln(abs(5*x + 3)) - 1331*l
n(abs(3*x + 2))