3.1186 \(\int \frac{1-2 x}{(2+3 x)^4 (3+5 x)} \, dx\)

Optimal. Leaf size=48 \[ \frac{55}{3 x+2}+\frac{11}{2 (3 x+2)^2}+\frac{7}{9 (3 x+2)^3}-275 \log (3 x+2)+275 \log (5 x+3) \]

[Out]

7/(9*(2 + 3*x)^3) + 11/(2*(2 + 3*x)^2) + 55/(2 + 3*x) - 275*Log[2 + 3*x] + 275*L
og[3 + 5*x]

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Rubi [A]  time = 0.0494828, antiderivative size = 48, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ \frac{55}{3 x+2}+\frac{11}{2 (3 x+2)^2}+\frac{7}{9 (3 x+2)^3}-275 \log (3 x+2)+275 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

7/(9*(2 + 3*x)^3) + 11/(2*(2 + 3*x)^2) + 55/(2 + 3*x) - 275*Log[2 + 3*x] + 275*L
og[3 + 5*x]

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Rubi in Sympy [A]  time = 7.69586, size = 42, normalized size = 0.88 \[ - 275 \log{\left (3 x + 2 \right )} + 275 \log{\left (5 x + 3 \right )} + \frac{55}{3 x + 2} + \frac{11}{2 \left (3 x + 2\right )^{2}} + \frac{7}{9 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-275*log(3*x + 2) + 275*log(5*x + 3) + 55/(3*x + 2) + 11/(2*(3*x + 2)**2) + 7/(9
*(3*x + 2)**3)

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Mathematica [A]  time = 0.0405569, size = 40, normalized size = 0.83 \[ \frac{8910 x^2+12177 x+4172}{18 (3 x+2)^3}-275 \log (3 x+2)+275 \log (-3 (5 x+3)) \]

Antiderivative was successfully verified.

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

[Out]

(4172 + 12177*x + 8910*x^2)/(18*(2 + 3*x)^3) - 275*Log[2 + 3*x] + 275*Log[-3*(3
+ 5*x)]

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Maple [A]  time = 0.013, size = 45, normalized size = 0.9 \[{\frac{7}{9\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{11}{2\, \left ( 2+3\,x \right ) ^{2}}}+55\, \left ( 2+3\,x \right ) ^{-1}-275\,\ln \left ( 2+3\,x \right ) +275\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

7/9/(2+3*x)^3+11/2/(2+3*x)^2+55/(2+3*x)-275*ln(2+3*x)+275*ln(3+5*x)

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Maxima [A]  time = 1.34666, size = 62, normalized size = 1.29 \[ \frac{8910 \, x^{2} + 12177 \, x + 4172}{18 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + 275 \, \log \left (5 \, x + 3\right ) - 275 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/18*(8910*x^2 + 12177*x + 4172)/(27*x^3 + 54*x^2 + 36*x + 8) + 275*log(5*x + 3)
- 275*log(3*x + 2)

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Fricas [A]  time = 0.20973, size = 101, normalized size = 2.1 \[ \frac{8910 \, x^{2} + 4950 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (5 \, x + 3\right ) - 4950 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 12177 \, x + 4172}{18 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/18*(8910*x^2 + 4950*(27*x^3 + 54*x^2 + 36*x + 8)*log(5*x + 3) - 4950*(27*x^3 +
54*x^2 + 36*x + 8)*log(3*x + 2) + 12177*x + 4172)/(27*x^3 + 54*x^2 + 36*x + 8)

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Sympy [A]  time = 0.361858, size = 41, normalized size = 0.85 \[ \frac{8910 x^{2} + 12177 x + 4172}{486 x^{3} + 972 x^{2} + 648 x + 144} + 275 \log{\left (x + \frac{3}{5} \right )} - 275 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(8910*x**2 + 12177*x + 4172)/(486*x**3 + 972*x**2 + 648*x + 144) + 275*log(x + 3
/5) - 275*log(x + 2/3)

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GIAC/XCAS [A]  time = 0.207678, size = 51, normalized size = 1.06 \[ \frac{8910 \, x^{2} + 12177 \, x + 4172}{18 \,{\left (3 \, x + 2\right )}^{3}} + 275 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 275 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/18*(8910*x^2 + 12177*x + 4172)/(3*x + 2)^3 + 275*ln(abs(5*x + 3)) - 275*ln(abs
(3*x + 2))