Optimal. Leaf size=26 \[ \frac{\log (b+x)}{a-b}-\frac{\log (a+x)}{a-b} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0205634, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{\log (b+x)}{a-b}-\frac{\log (a+x)}{a-b} \]
Antiderivative was successfully verified.
[In] Int[1/((a + x)*(b + x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.79153, size = 15, normalized size = 0.58 \[ - \frac{\log{\left (a + x \right )}}{a - b} + \frac{\log{\left (b + x \right )}}{a - b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+x)/(b+x),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00975916, size = 19, normalized size = 0.73 \[ \frac{\log (b+x)-\log (a+x)}{a-b} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a + x)*(b + x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 27, normalized size = 1. \[ -{\frac{\ln \left ( a+x \right ) }{a-b}}+{\frac{\ln \left ( b+x \right ) }{a-b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+x)/(b+x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.36114, size = 35, normalized size = 1.35 \[ -\frac{\log \left (a + x\right )}{a - b} + \frac{\log \left (b + x\right )}{a - b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + x)*(b + x)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.221043, size = 27, normalized size = 1.04 \[ -\frac{\log \left (a + x\right ) - \log \left (b + x\right )}{a - b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + x)*(b + x)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.28664, size = 80, normalized size = 3.08 \[ \frac{\log{\left (- \frac{a^{2}}{2 \left (a - b\right )} + \frac{a b}{a - b} + \frac{a}{2} - \frac{b^{2}}{2 \left (a - b\right )} + \frac{b}{2} + x \right )}}{a - b} - \frac{\log{\left (\frac{a^{2}}{2 \left (a - b\right )} - \frac{a b}{a - b} + \frac{a}{2} + \frac{b^{2}}{2 \left (a - b\right )} + \frac{b}{2} + x \right )}}{a - b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+x)/(b+x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.21192, size = 38, normalized size = 1.46 \[ -\frac{{\rm ln}\left ({\left | a + x \right |}\right )}{a - b} + \frac{{\rm ln}\left ({\left | b + x \right |}\right )}{a - b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((a + x)*(b + x)),x, algorithm="giac")
[Out]