3.380 \(\int \frac{x}{13+\frac{2}{x}+15 x} \, dx\)

Optimal. Leaf size=26 \[ \frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1) \]

[Out]

x/15 - (4*Log[2 + 3*x])/63 + Log[1 + 5*x]/175

_______________________________________________________________________________________

Rubi [A]  time = 0.0444354, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1) \]

Antiderivative was successfully verified.

[In]  Int[x/(13 + 2/x + 15*x),x]

[Out]

x/15 - (4*Log[2 + 3*x])/63 + Log[1 + 5*x]/175

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 10.9559, size = 20, normalized size = 0.77 \[ \frac{x}{15} - \frac{4 \log{\left (3 x + 2 \right )}}{63} + \frac{\log{\left (5 x + 1 \right )}}{175} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x/(13+2/x+15*x),x)

[Out]

x/15 - 4*log(3*x + 2)/63 + log(5*x + 1)/175

_______________________________________________________________________________________

Mathematica [A]  time = 0.00706266, size = 26, normalized size = 1. \[ \frac{x}{15}-\frac{4}{63} \log (3 x+2)+\frac{1}{175} \log (5 x+1) \]

Antiderivative was successfully verified.

[In]  Integrate[x/(13 + 2/x + 15*x),x]

[Out]

x/15 - (4*Log[2 + 3*x])/63 + Log[1 + 5*x]/175

_______________________________________________________________________________________

Maple [A]  time = 0.008, size = 21, normalized size = 0.8 \[{\frac{x}{15}}-{\frac{4\,\ln \left ( 2+3\,x \right ) }{63}}+{\frac{\ln \left ( 1+5\,x \right ) }{175}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x/(13+2/x+15*x),x)

[Out]

1/15*x-4/63*ln(2+3*x)+1/175*ln(1+5*x)

_______________________________________________________________________________________

Maxima [A]  time = 0.814758, size = 27, normalized size = 1.04 \[ \frac{1}{15} \, x + \frac{1}{175} \, \log \left (5 \, x + 1\right ) - \frac{4}{63} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(15*x + 2/x + 13),x, algorithm="maxima")

[Out]

1/15*x + 1/175*log(5*x + 1) - 4/63*log(3*x + 2)

_______________________________________________________________________________________

Fricas [A]  time = 0.262954, size = 27, normalized size = 1.04 \[ \frac{1}{15} \, x + \frac{1}{175} \, \log \left (5 \, x + 1\right ) - \frac{4}{63} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(15*x + 2/x + 13),x, algorithm="fricas")

[Out]

1/15*x + 1/175*log(5*x + 1) - 4/63*log(3*x + 2)

_______________________________________________________________________________________

Sympy [A]  time = 0.230857, size = 20, normalized size = 0.77 \[ \frac{x}{15} + \frac{\log{\left (x + \frac{1}{5} \right )}}{175} - \frac{4 \log{\left (x + \frac{2}{3} \right )}}{63} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(13+2/x+15*x),x)

[Out]

x/15 + log(x + 1/5)/175 - 4*log(x + 2/3)/63

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.262967, size = 30, normalized size = 1.15 \[ \frac{1}{15} \, x + \frac{1}{175} \,{\rm ln}\left ({\left | 5 \, x + 1 \right |}\right ) - \frac{4}{63} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x/(15*x + 2/x + 13),x, algorithm="giac")

[Out]

1/15*x + 1/175*ln(abs(5*x + 1)) - 4/63*ln(abs(3*x + 2))