3.1185 \(\int \frac{1-2 x}{(2+3 x)^3 (3+5 x)} \, dx\)

Optimal. Leaf size=37 \[ \frac{11}{3 x+2}+\frac{7}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (5 x+3) \]

[Out]

7/(6*(2 + 3*x)^2) + 11/(2 + 3*x) - 55*Log[2 + 3*x] + 55*Log[3 + 5*x]

_______________________________________________________________________________________

Rubi [A]  time = 0.0443608, antiderivative size = 37, 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 \[ \frac{11}{3 x+2}+\frac{7}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (5 x+3) \]

Antiderivative was successfully verified.

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

[Out]

7/(6*(2 + 3*x)^2) + 11/(2 + 3*x) - 55*Log[2 + 3*x] + 55*Log[3 + 5*x]

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 6.68312, size = 32, normalized size = 0.86 \[ - 55 \log{\left (3 x + 2 \right )} + 55 \log{\left (5 x + 3 \right )} + \frac{11}{3 x + 2} + \frac{7}{6 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-55*log(3*x + 2) + 55*log(5*x + 3) + 11/(3*x + 2) + 7/(6*(3*x + 2)**2)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0523764, size = 35, normalized size = 0.95 \[ \frac{198 x+139}{6 (3 x+2)^2}-55 \log (3 x+2)+55 \log (-3 (5 x+3)) \]

Antiderivative was successfully verified.

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

[Out]

(139 + 198*x)/(6*(2 + 3*x)^2) - 55*Log[2 + 3*x] + 55*Log[-3*(3 + 5*x)]

_______________________________________________________________________________________

Maple [A]  time = 0.01, size = 36, normalized size = 1. \[{\frac{7}{6\, \left ( 2+3\,x \right ) ^{2}}}+11\, \left ( 2+3\,x \right ) ^{-1}-55\,\ln \left ( 2+3\,x \right ) +55\,\ln \left ( 3+5\,x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

7/6/(2+3*x)^2+11/(2+3*x)-55*ln(2+3*x)+55*ln(3+5*x)

_______________________________________________________________________________________

Maxima [A]  time = 1.34826, size = 49, normalized size = 1.32 \[ \frac{198 \, x + 139}{6 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + 55 \, \log \left (5 \, x + 3\right ) - 55 \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*(198*x + 139)/(9*x^2 + 12*x + 4) + 55*log(5*x + 3) - 55*log(3*x + 2)

_______________________________________________________________________________________

Fricas [A]  time = 0.215653, size = 74, normalized size = 2. \[ \frac{330 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 330 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 198 \, x + 139}{6 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*(330*(9*x^2 + 12*x + 4)*log(5*x + 3) - 330*(9*x^2 + 12*x + 4)*log(3*x + 2) +
198*x + 139)/(9*x^2 + 12*x + 4)

_______________________________________________________________________________________

Sympy [A]  time = 0.305841, size = 31, normalized size = 0.84 \[ \frac{198 x + 139}{54 x^{2} + 72 x + 24} + 55 \log{\left (x + \frac{3}{5} \right )} - 55 \log{\left (x + \frac{2}{3} \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(198*x + 139)/(54*x**2 + 72*x + 24) + 55*log(x + 3/5) - 55*log(x + 2/3)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.212718, size = 45, normalized size = 1.22 \[ \frac{198 \, x + 139}{6 \,{\left (3 \, x + 2\right )}^{2}} + 55 \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - 55 \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*(198*x + 139)/(3*x + 2)^2 + 55*ln(abs(5*x + 3)) - 55*ln(abs(3*x + 2))