Optimal. Leaf size=11 \[ \log (x)-\log (1+b x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.273, Rules used = {36, 29, 31}
\begin {gather*} \log (x)-\log (b x+1) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 29
Rule 31
Rule 36
Rubi steps
\begin {align*} \int \frac {1}{x (1+b x)} \, dx &=-\left (b \int \frac {1}{1+b x} \, dx\right )+\int \frac {1}{x} \, dx\\ &=\log (x)-\log (1+b x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \log (x)-\log (1+b x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Mathics [A]
time = 1.58, size = 11, normalized size = 1.00 \begin {gather*} \text {Log}\left [x\right ]-\text {Log}\left [\frac {1}{b}+x\right ] \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.09, size = 12, normalized size = 1.09
method | result | size |
default | \(\ln \left (x \right )-\ln \left (b x +1\right )\) | \(12\) |
norman | \(\ln \left (x \right )-\ln \left (b x +1\right )\) | \(12\) |
meijerg | \(\ln \left (x \right )+\ln \left (b \right )-\ln \left (b x +1\right )\) | \(14\) |
risch | \(\ln \left (-x \right )-\ln \left (b x +1\right )\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.24, size = 11, normalized size = 1.00 \begin {gather*} -\log \left (b x + 1\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.31, size = 11, normalized size = 1.00 \begin {gather*} -\log \left (b x + 1\right ) + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 8, normalized size = 0.73 \begin {gather*} \log {\left (x \right )} - \log {\left (x + \frac {1}{b} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 12, normalized size = 1.09 \begin {gather*} \ln \left |x\right |-\ln \left |x b+1\right | \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.10, size = 9, normalized size = 0.82 \begin {gather*} -2\,\mathrm {atanh}\left (2\,b\,x+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________