Optimal. Leaf size=19 \[ -b \log (x)+b \log (b x+1)-\frac{1}{x} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0221505, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -b \log (x)+b \log (b x+1)-\frac{1}{x} \]
Antiderivative was successfully verified.
[In] Int[1/(x^2*(1 + b*x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.66987, size = 15, normalized size = 0.79 \[ - b \log{\left (x \right )} + b \log{\left (b x + 1 \right )} - \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(b*x+1),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00548739, size = 19, normalized size = 1. \[ -b \log (x)+b \log (b x+1)-\frac{1}{x} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^2*(1 + b*x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 20, normalized size = 1.1 \[ -{x}^{-1}-b\ln \left ( x \right ) +b\ln \left ( bx+1 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(b*x+1),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33624, size = 26, normalized size = 1.37 \[ b \log \left (b x + 1\right ) - b \log \left (x\right ) - \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + 1)*x^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.212271, size = 28, normalized size = 1.47 \[ \frac{b x \log \left (b x + 1\right ) - b x \log \left (x\right ) - 1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + 1)*x^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.12722, size = 14, normalized size = 0.74 \[ b \left (- \log{\left (x \right )} + \log{\left (x + \frac{1}{b} \right )}\right ) - \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(b*x+1),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.209177, size = 28, normalized size = 1.47 \[ b{\rm ln}\left ({\left | b x + 1 \right |}\right ) - b{\rm ln}\left ({\left | x \right |}\right ) - \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x + 1)*x^2),x, algorithm="giac")
[Out]